Cleaver and the Mansell management team all signed contracts to stay at the firm. However, Building understands Cleaver is hoping to leave the £530m-turnover group.
Market sources claimed that Cleaver was likely to leave by the end of next year. One said: "I expect him to leave in a matter of months rather than years."
Another source added: "Philip will stay as long as Balfour Beatty needs him, which I don't think will be that long."
Neither Cleaver nor Balfour Beatty would be drawn on the subject. Cleaver said: "The Mansell sale was conditional on my signing a new contract, which I have signed."
A Balfour Beatty spokesperson said: "The management are part of the deal and we look forward to working with them." On Cleaver's departure he added: "We have no observation on such speculation."
Balfour Beatty beat off a joint venture of Middle Eastern contractors to buy Mansell.
Mansell had wanted to float on the stock exchange but had been hampered by a £30m pension deficit that reduced the value of the firm from £55m to £42m.
The sale was received with surprise by analysts who had seen Balfour Beatty's growth in international rather than domestic markets. Balfour Beatty last year tried to buy American contractor JA Jones but failed because of a drop in its share price.
Balfour Beatty declared the offer for Mansell unconditional last week. The deal will now be investigated by the Office of Fair Trading, which could refer it to the Competition Commission.
A spokesperson for the OFT said that a decision on referral would be made early next year.