Luka Modric's desire to force a transfer to Real Madrid has been complicated by interest from Paris St-Germain, who have indicated that they would be prepared to pay Tottenham Hotspur's asking price of £40m.

The Croatia midfielder has no desire to join PSG, despite their big spending and ambitions to build a team to compete in the Champions League, but the French club's willingness to pay the figure that Tottenham have demanded has served to harden the conviction at White Hart Lane to hold out for their price in the stand-off with Madrid.

The Spaniards know they are the preferred choice of Modric, whose behaviour at the end of last week incensed the Tottenham hierarchy and has drawn a public rebuke from the manager, André Villas-Boas, who described it as "not professional".

Modric refused to train last Friday and he further disobeyed orders on Saturday when he failed to report for the flight to Los Angeles, where the club have begun their three-city tour of the United States. Tottenham intend to fine him two weeks' wages, a sum of £80,000.

Modric has now started to train at Spurs Lodge in Essex - he reported on Monday and Tuesday - as he seeks to build his fitness. He stood to be fined further if he had remained away. Modric trained alongside Steven Pienaar, who is expected to move back to Everton on a permanent transfer.

Madrid feel that they can make capital out of Modric's rebellion, even if it has been diluted slightly by his presence back at Spurs Lodge, where the players whom Villas-Boas has not taken to the US continue to train, pending the official move to the club's new training base in Bulls Cross.

Madrid have so far offered a package to Tottenham for Modric that could be worth £31m, if the add-ons are realised. They believe that, if the player no longer wants to represent Tottenham and has instead made it clear that he wants to join them, they ought to be able to haggle the price down. They contend that Modric is no longer of top value to Tottenham.

Tottenham have little time for Madrid's argument but the attitude of the chairman, Daniel Levy, has changed, in that he is prepared to sell Modric for what he feels is the right price. Last summer he refused categorically to sanction Modric's proposed £40m move to Chelsea, even after he had submitted a transfer request.

But if Madrid do not pay the money, Levy is prepared to keep Modric, who is under contract until 2016. Modric refocused last September after his Chelsea move had been blocked to enjoy an excellent season and Levy would expect the same from him again if a deal cannot be concluded to his satisfaction.

Madrid's assistant coach, Aitor Karanka, has confirmed the club's interest in Modric, telling the Spanish newspaper AS: "Which club would not want a player like him? He is an outstanding footballer and had a great tournament [Euro 2012]. It is clear that he would fit in Madrid."

Villas-Boas's problems in midfield extend to the fitness of Scott Parker, who has suffered complications with the achilles injury that he felt towards the end of last season. Parker is working at Spurs Lodge and the club still hope to avoid the need for an operation, although Villas-Boas fears the worst.

Surgery could keep Parker out for six weeks, meaning that he would miss the start of the season. Tottenham kick off away to Newcastle United on 18 August. Parker may also be a doubt for England's first two World Cup qualifiers, against Moldova on 7 September and Ukraine on 11 September.

Tottenham completed the signings of the defender Jan Vertonghen from Ajax and the midfielder Gylfi Sigurdsson from Hoffenheim in the days after they unveiled Villas-Boas as their new manager on 3 July, but it seems as though their momentum on the transfer market has been checked.

They have been close to the permanent signing of the striker Emmanuel Adebayor from Manchester City for some time but they have not yet finalised his personal terms. Villas-Boas has said that he is not in the market for a new goalkeeper, which may or may not be a ruse to force Hugo Lloris to reduce his demands.

Villas-Boas has monitored the Lyon goalkeeper but Tottenham have been put off by the financial package that would be required to secure his signature. Villas-Boas said that he was ready to put his faith in the club's experienced goalkeepers Brad Friedel, Heurelho Gomes and Carlo Cudicini.

"The search for a goalkeeper at the moment is a non-search because we have three top goalkeepers and we have David Button coming through and wanting to join a group of three excellent goalkeepers," Villas-Boas said. "So it's nonexistent and it's false that we are at the moment looking for a goalkeeper."