The busiest place at Elland Road is the treatment room. Tony Yeboah, Brian Deane, Lee Bowyer now Ian Rush. Reports are not encouraging. "I don't know how close we are to having them back," Graham added.
Last week the Leeds manager made a fruitless trip abroad (a strong defender is the urgent priority). Eager to sign new players, he has money available but not yet the inclination to spend. And in any case, Graham's ideal is a team built around British qualities with a touch of foreign flair thrown in for good measure.
Bearing this in mind, the problem Graham went on to speak about will be familiar to many managers in the Premiership. "I kept closely in touch with the game when I was out of it for a year, but as soon as I got to Leeds and started looking around again in earnest it dawned on me that there aren't any quality players available in this country," he said. "David Pleat was saying that the other day and he is absolutely right. All the best players are tied up with a small group of clubs and, understandably, they don't want to release them."
So, struggling along with his injury list, Graham had five boys in the team at Leicester, three teenagers among his substitutes.
As a callow youth himself signed from Aston Villa ("George was doomed until I went for him," Tommy Docherty once said wickedly), Graham figured prominently in an exciting Sixties Chelsea team which Docherty liked to call "my young diamonds" - Terry Venables, John Hollins, Ron Harris, Bobby Tambling, Barry Bridges, Peter Bonetti. The circumstances, however, were different. "At that time Chelsea had a terrific scouting system but even so it was exceptional that so many good players came through at the same time," Graham said.
It remains to be seen how many of the Leeds crop will establish themselves in the game but as Graham says he has to be fair to them. "At least I'm getting an opportunity to look at their potential and I can't complain about what they are putting into it," he said.
A great deal of effort went into the pattern Leeds adopted but another defeat means that Graham has lost three League games in 20 days since succeeding Howard Wilkinson. The impression you get is that it has turned out to be a more difficult task than he imagined.
A point with which he agrees is that too much is being made about the quality of football in the Premiership. "The supporters may find it exciting," he said, "but there are only a handful of good teams."
Leeds are a long way from being one of them. A five-man defence was too easily penetrated from midfield and even allowing for lack of support Lee Sharpe was a big disappointment.
If they are not likely to quicken the pulse with their essentially direct method, Leicester had a better idea of what is required to win matches. Capitalising on Leeds's lack of experience, Mustafa Izzet set off on enterprising runs and Leicester should have been ahead before Emile Heskey scored after an hour. The manner of it did not improve Graham's humour. Neil Lennon got past David Wetherall easily and Richard Jobson made a complete hash of a chance to clear when Nigel Martyn palmed the ball across goal. Heskey will get few more simple opportunities.
Ian Harte's splendid header against the crossbar was one thing Graham could look back on with some satisfaction - "we've hit the woodwork three times including when we lost 1-0 to Newcastle," he said - but back at home in London yesterday he was busy on the telephone.
"I've got to get players from somewhere," he said. The weekend's results, particularly Middlesbrough's heavy defeat at Southampton renewed his belief that the solution does not rest with foreign imports. "Buy British" is his motto. The trouble is that he cannot see much out there.
Goal: Heskey (60) 1-0.
Leicester City (5-3-1-1): Keller; Grayson, Whitlow, Watts, Walsh, Prior; Izzet, Lennon, Taylor; Marshall (Parker 76); Heslop. Substitutes not used: Lawrence, Lewis, Robins, Poole (gk).
Leeds United (5-3-2): Martyn; Kelly, Wetherall, Palmer, Jobson, Harte; Jackson, Ford, Couzens (Radebe, 83); Sharpe, Wallace. Substitutes not used: Blunt, Boyle, Kewell, Beeney (gk).
Referee: S W Dunn (Bristol).
Bookings: Leicester: Grayson. Leeds: Jackson, Wetherall, Palmer.
Man of the match: Palmer. Attendance: 20,359.