The 38-year-old striker is available on a free transfer in the new year following the completion of his two-year spell at LA Galaxy.
Mourinho signed Ibrahimovic, also on a free transfer, for Manchester United in 2016, with the Swede scoring 26 goals in 46 appearances before a serious knee threatened to end his career.
Ibrahimovic left United in March 2018 but maintains a strong relationship with Mourinho, who first worked with him at Inter Milan and values his professionalism and winning mentality.
Tottenham have not replaced Fernando Llorente and, therefore, do not have an understudy to Harry Kane. It could be a role ideally suited to Ibrahimovic at this stage of his career as he returns to European football.
United have ruled out bringing Ibrahimovic back to Old Trafford and it is understood his agent, Mino Raiola, has been in contact with a number of Italian clubs, headed by Milan which was the last Serie A club he played for before joining Paris St-Germain.
Italian sources say Raiola held talks with Milan on Wednesday. The suggestion was that Ibrahimovic’s wage demands might have been a stumbling block.
Spurs are unlikely to want to damage their pay structure to bring him back to the Premier League but there is believed to be interest from them following Mourinho’s arrival.
Signing Ibrahimovic, if Spurs went ahead with it, would only be a short-term measure which may not appeal to him as it is understood he is seeking an 18-month deal with a European club.
But it may appeal to his ego and sense of drama to join Spurs, who have not won a trophy since 2008, and to do so with Mourinho.
At the same time, he would be unlikely to be a regular starter, given Kane’s status at Spurs and with Mourinho and the hierarchy acutely aware that the England captain is unsettled and may consider his future in the summer should they fail to win silverware and also do not qualify for Champions League football.
Spurs’ new head coach is unlikely to push for the deal to be completed,
having assured chairman Daniel Levy that he would not be demanding in the transfer market.
He has also told Levy that his priority is sorting out the Spurs defence, but he could regard the much-decorated Ibrahimovic as a short-term help to a squad that has not yet won a trophy.
Mourinho reiterated at his unveiling that he did not want new players, having already shown his regard for the current squad by having tried to sign certain members in the past.
“I told them that one of the reasons why I decided to come was the players,” he said. “I tried to buy some of them for different clubs and I couldn’t.
“Some of them I didn’t even try because you know how impossible it is.
“But I like this squad very, very much. I like the players very, very much. It’s not something new that I said that.
“It’s not like ‘OK, now you are their manager you are saying that because you want to look nice’. That’s not the point.
“I don’t want to make big changes. I want to respect the base and the base is the work they did for 5½ years [under Mauricio Pochettino].”