With Robbie Fowler still needing treatment for a back problem, the two strikers seem likely to start the opening game of the season against West Bromwich on 6 August.
Vassell, 25, made his bow in the 2-1 victory at Stoke in a friendly on Saturday following his £2m move from Aston Villa. He played just over an hour at the Britannia Stadium, where City came from behind to chalk up a victory against the Championship side.
Cole cancelled out the opener from the Stoke trialist Bruce Dyer, with Bradley Wright-Phillips getting the winner.
Pearce said: "Darius did OK. He needs to get his fitness levels up. He has played only 45 minutes this pre-season for Villa. He will need time to bed in as he has been at another club for a long time and is leaving an environment where he grew up.
"It is not going to happen overnight. Andy Cole is also new and they will need time to gel. But some of the things I have seen in training between the pair makes me think this could be a nice partnership."
Meanwhile, Pearce has confirmed that Joey Barton will be given all the time he needs to reap the benefits of lifestyle coaching. The 22-year-old midfielder is due to start a programme of counselling following an incident in the team hotel in Thailand.
Barton was fined eight weeks' wages after he was sent home early from the City tour. He allegedly lashed out at a 15-year-old Everton fan and then his team-mate Richard Dunne when he intervened.
Pearce said: "I have told Joey to go away from the club until we get this lifestyle coaching organised. Once we get that in place, he can go away on that course and come back and join us while it is on-going.
"The most important thing is the long-term rehab of Joey. If I have to lose him for one, two, three, 10 games to make sure I have a better man and a better player I am happy to do that."
Yesterday, City drew 1-1 with Sheffield Wednesday at Hillsborough. Glenn Whelan opened the scoring for Wednesday in the 37th minute.
But City's bright young strikers are giving Pearce a boost ahead of the new season. And the Irishman Karl Bermingham, 19, brought the visitors level in the 61st minute.
City fielded a young side with only Danny Mills, Sylvain Distin and Stephen Jordan being regulars in the first team.