The Blues' striker is in advanced talks with Major League Soccer's DC United over a big-money move to become their marquee signing in July, as the Washington club prepare to move into a new stadium.
Wayne Rooney's return to boyhood club Everton was seen as the flawless way for an England icon in the twilight of his career to see-out the remainder of his playing days.
DC United are rock-bottom of the MLS Eastern Conference table with five points from seven games.
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Rooney is unlikely to be guaranteed regular football next season and is keen to make the move once the current campaign concludes on Sunday.
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If Rooney has already played his final game in the Premier League, he will leave as the second highest scorer in its history with 208 goals to his name, behind only the legendary Alan Shearer.
"If any players want to leave, I'm always comfortable with any player who wants to leave or if any player doesn't want to leave". If any player wants to leave they can go.
Allardyce said: "How as a manager can you guarantee anyone to play?" "It's up to the player to put their game together on a consistent basis every week and keep their place in the team".
Allardyce's own situation is also uncertain following supporter unrest at recent performances but the 63-year-old showed every intention of staying at the club next season.
"He appears to be level-headed and is one of those players who has not got carried away with it and I think that is probably why he has done so much, and played so well and achieved so much".
"Lampard, [Patrick] Vieira. now you have Zlatan [Ibrahimovic], you have Wayne, so I hope he enjoys [it]", Mourinho said.
Two weeks after indicating that he was staying at Goodison Park because he had discussed plans for pre-season with the club's leading shareholder, Allardyce said that he would find out the billionaire businessman's "thinking" during their meeting.