The Sunday Mirror says Pompey have ordered Mbesuma to lose at least a stone and a half before they will even consider him for first-team action.
The Zambian striker, signed for £750,000 from South African side Kaizer Chiefs, could also face a club fine for failing to adhere to a strict diet he was put on. He is expected to be sidelined for six weeks.
Mbesuma had to seek refuge in a Zambian police station on Thursday after fans witnessed him drinking ahead of a World Cup qualifying game against Senegal and threatened to beat him up.
Bolton boss Sam Allardyce pulled out of a deal to sign Mbesuma in the summer. The player would not have a weeks trial for staff to assess his fitness levels and Allardyce was not prepared to take the risk after having made this mistake once in the past.