Jose Mourinho wants to become the new Spurs boss after Mauricio Pochettino was sensationally sacked on Tuesday night.
The ex-Manchester United boss - now a free agent - is open to talks after the north Londoners sent shock waves throughout Europe by cutting the man that led them to last season’s Champions League loose.
Contact has not yet been made but Levy is expected to explore the option as he faces paying up £12.5million-a-year Pochettino and his staff.
Levy blamed the club’s poor run of form either side of the summer for the decision.
Despite reaching the knockout stages of the Champions League, Spurs sit 14th in the Premier League having won just three times this season.
Levy said: “Regrettably domestic results at the end of last season and the beginning of this season have been extremely disappointing.
“It falls on the board to make the difficult decisions - this one made more so given the many memorable moments we have had with Mauricio and his coaching staff - but we do so in the club's best interests.”
Pochettino and his staff - assistant Jesus Perez, and coaches Miguel d'Agostino and Antoni Jimenez - have also left the club. They all had three and a half years left on their contracts.
Pochettino guided Tottenham to the League Cup final in his first full season while two third-placed finishes sandwiched a runners-up spot in the Premier League in 2017.
As well as leading Spurs to a runners-up finish in last season's Champions League he also took them to fourth in the league.
He also had to contend with playing home games at Wembley for 18 months while the club's new ground was built and his impressive results despite this led to links with Real Madrid and Manchester United .
But as well as their disappointing league form, they were knocked out of the League Cup by League Two side Colchester and hammered 7-2 by Bayern Munich in the Champions League.
"Mauricio and his coaching staff will always be part of our history," added Levy.
"I have the utmost admiration for the manner in which he dealt with the difficult times away from a home ground whilst we built the new stadium and for the warmth and positivity he brought to us.
"I should like to thank him and his coaching staff for all they have contributed. They will always be welcome here.
"We have a talented squad. We need to re-energise and look to deliver a positive season for our supporters."