The mercurial Swede is due to complete a two-year spell with L.A. Galaxy in the MLS and has been linked with a move to Serie A.
Ibrahimovic's agent, Mino Raiola, has reportedly been negotiating a switch to one of the player's former teams, AC Milan, but north London could emerge as the his latest destination.
Spurs have experienced a poor start to the season, leading to Tuesday's dismissal of coach Mauricio Pochettino.
Mourinho was appointed as manager with no time wasted, and the Portuguese has been tasked to lift Spurs from their lowly Premier League position of 14th.
The Lilywhites have been reliant on Harry Kane's goals and inspiration in recent years, but Ibrahimovic could share the load.
The 38-year-old continues to be a prolific force, scoring 53 goals and providing 17 assists in two MLS seasons.
Spurs remain short in the striking department after the departure of Fernando Llorente to Napoli on a free transfer in September.
Mourinho's new club are close to securing qualification for the UEFA Champions League knockouts, and Ibrahimovic could be attracted to appearing in Europe's biggest competition once again.