The most optimistic prognosis is that both singles finals will be played on Sunday. The only time that has happened was in 1989, when Steffi Graf defeated Martina Navratilova and Boris Becker completed a German double with victory against Stefan Edberg.
The year before, Becker had also taken part in the only men's singles final since 1922 to be staged on a Monday. In 1988, Becker lost to Edberg.
As the covers dripped with rain last night, the All England Club contemplated a weather forecast that was "fair on Friday, but not so good on Saturday and Sunday".
Mills said: "We have to be fair and even-handed to all concerned. The weather has made it difficult. Lindsay Davenport, for example, has still to play potentially nine matches in three events.
"We are considering moving the ladies final to Sunday, with the quarter- finals completed tomorrow, the semi-finals on Saturday and the final on Sunday. The same applies to the men's championships.
Mills added that he would be speaking to the women competitors individually. "I do not intend to discuss the situation with all of them," he said. "I don't think it's fair at this stage of a Grand Slam tournament to put that pressure on them, one way or another."
Glorious weather during the first week of this year's championships attracted record attendances. There was no reason to contemplate the last resort of playing on the middle Sunday, which happened in 1991 and 1997.
Last Tuesday's wash-out was overcome when mainly dry weather on Wednesday enabled the programme to catch up with the schedule. This included Tim Henman's dramatic five sets victory against the American Jim Courier, which started on Monday.
The 16 singles quarter-finals, eight men's matches and eight women's, needed to be completed yesterday, but only one player was able to advance to the semi-finals before the rain break the dominated the day. That was the American Lindsay Davenport, who defeated Jana Novotna, the defending champion.
The only other quarter-final to have reached a final set by 7.30pm was the encounter involving Graf and the American Venus Williams. Graf and Williams are in the opposite section of the draw to Davenport.
Henman's rain-delayed week was again put on hold. Only eight minutes of the No 6 seed's quarter-final against the Frenchman Cedric Pioline on Court No 1 was possible, and that was after several false starts.
Jimmy Hill was among the spectators hoping to see the match of the day, but for most of the afternoon it seemed that the football pundit would have to settle for knock-up of the day.
A huge dark cloud settled over the court the moment it was vacated by Davenport. Henman and Pioline arrived at 3.18 pm to a rousing reception. Six minutes later, having come close to completing their warm-up, they were sent back to the locker-room.
The covers were removed again at 4.24 pm, only to be dragged back across the court after two minutes, before Henman and Pioline had time to peek outside. The covers were removed a third time at 4.27pm, and when there was no sign of the players, the frustrated spectators began a slow hand- clap.
Told that play would resume after 15 minutes, provided there was no further rain, the crowd settled down. They broke into cheers when Henman and Pioline walked back on the court at 4.45pm. The Australian umpire, Wayne McKewen, took his place in the chair, the knock-up was completed, and Henman struck the first ball at 4.53pm (Pioline had elected to receive).
Henman held to 15, starting off with an ace clocked at 116mph. He then netted a forehand before winning the next three points. The British No 2 then took Pioline to a couple of deuces, at which point play was suspended at 5.02pm.
With no possibility of finishing the Henman-Pioline match, it was decided to switch the women's quarter-final between Nathalie Tauziat and Mirjana Lucic to Court No 1 from Court No 18. Tauziat would have been serving for the first set at 5-4, but the players did not make an appearance. Tony Gathercole, the assistant referee, said one of the players refused to move court.
The latest ever Wimbledon finish was the first meeting held at Church Road in 1922, when there was rain every single day. Only the Centre Court had a tarpaulin, so the outside courts became a quagmire, especially during the second week. On three consecutive days only 11 matches were played, and the tournament finally concluded on the third Wednesday. Only twice has play stretched as far as the third Tuesday, in 1919 and 1927.
THE WIMBLEDON RAIN GAME
The programme was extended until the Tuesday of the third week due to rain.
The first meeting at Church Road saw rain every day. With only the Centre Court covered by a tarpaulin, the grounds became a bog. The tournament eventually ended on the Wednesday of the third week, the latest ever finish.
After the first Monday, there was not a day without heavy rain. Play eventually finished on the third Tuesday.
A cold and miserable tournament, with the second Saturday washed out. The women's final was played on the third Monday for the first time.
Rain washed out the second Saturday and there were four Sunday finals for the first time.
The men's final was played on a Monday for the first (and only) time since 1922 after a week of sun was followed by a week of rain interruptions. Stefan Edberg beat Boris Becker.
Rain delayed the last three days and the men's and women's finals were both played on a Sunday for the first (and only) time. Boris Becker beat Stefan Edberg and Steffi Graf beat Martina Navratilova. The mixed doubles final was played on the third Monday.
A week of fine weather was followed by a week of wet. The tournament concluded on the third Monday with the men's doubles. John McEnroe (with Michael Stich) won his last Grand Slam title that day.
Mixed weather in the first week was followed by rain in the second. The programme concluded on the third Monday with the women's doubles, when Martina Hingis became the youngest-ever adult title winner at Wimbledon, aged 15 years 282 days.