Modric boarded a flight to London from Zagreb on Wednesday afternoon ahead of a meeting he has scheduled with his agent and Levy on Wednesday night.
Shortly after rejecting a ?22million bid from Chelsea for Croatia international Modric, Levy issued a statement insisting that the Spurs playmaker is not for sale at any price.
There is nothing to suggest that his stance has softened at all during the three weeks that have passed since the bid, despite Modric's public assertion that he wants to leave for Stamford Bridge.
It is understood that Levy is determined to hang on to the 25-year-old, who was a key part of Tottenham's European and domestic campaigns last term, regardless of whether he wants to leave.
Modric himself gave little away as he waited to board the plane in his homeland, saying: "Today I have a flight to London and tomorrow I start training. I have an appointment to meet the chairman, but we will see."
But when asked about the possibility of joining Chelsea, Modric said: "Anything is possible."
Modric spoke of Chelsea in glowing terms when he went on the record to talk about his desire to move to Stamford Bridge last month, describing the Blues as a "great" and "ambitious" club capable of competing for silverware.
The mere suggestion that he would not be able to fulfil his ambitions at White Hart Lane has infuriated Spurs fans, but despite their angst, Levy is determined not to sell him.
The Tottenham chairman is conscious of the effect that selling Modric could have on the team given that he played such an important role in the club's remarkable run to the Champions League quarter-finals last term.
He could offer Modric a new contract to persuade him to stay, despite the former Dinamo Zagreb player being just 12 months into a six-year contract he signed in 2010.
The diminutive midfielder scored just four goals last season, but provided countless assists and performed tirelessly, reportedly attracting the attention of Manchester United as well as Chelsea in the process.
Tottenham boss Harry Redknapp admits that his attempt to get the club back into the Champions League will suffer if Modric is sold.
"It's difficult when crazy sums of money are being bandied about but we need to keep Luka and all our best players if we are to improve," Redknapp told the London Evening Standard.
"If we want to continue to challenge the top clubs in the Premier League then we simply have to get stronger - not weaker.
"Luka is a fantastic player and we need to keep him at the club. We certainly don't want to sell him."
New Blues boss Andre Villas-Boas led his first full training session at Chelsea's Cobham base today and will assess whether he thinks the squad needs strengthening over the next few days.
Modric, meanwhile, is due to join the rest of his Spurs team-mates at training tomorrow for the first time since the transfer saga surrounding him began.
Source: Team Talk
Source: Team Talk