Chelsea have had a £22m offer for Luka Modric rejected by Tottenham Hotspur, according to reports last night, in a move that could ignite a bidding war between the Premier League's three richest clubs as Manchester City and Manchester United also retain a keen interest in the Croatian playmaker.

The formal approach by Roman Abramovich, the Chelsea owner, was made late yesterday afternoon but was rejected without consideration by the Tottenham chairman, Daniel Levy. While he may wish to keep Modric, who is considered the club's best player alongside Gareth Bale, and has publicly said alongside Harry Redknapp, the manager, that there is no desire to sell any of the club's premier players this summer, Levy has also proved a canny operator in the transfer market.

He may be waiting to see who else joins the race to sign the 25-year-old with Levy shrewd enough to acknowledge that the growing interest in a player dubbed "Little Mozart", due to his sublime talent, could ultimately prove impossible to keep him at White Hart Lane.

Unlike last season Tottenham will not be featuring in the Champions League during the next campaign and Modric's preference is to continue playing in club football's elite competition.

While his agent could not be reached last night Modric recently conceded that his future was unsure. "I'm a Tottenham player and will be in London on July 7 to begin preparing for the season," he said. "But I want to say that transfers could occur later. In England it is often the case they happen on the last day of the transfer period, August 31. So it is pointless to worry about anything now. If my situation changes after the start of preparation, it would not be a problem. You can't predict things in football because anything can happen. But I am enjoying it here."

Although Abramovich has yet to appoint a successor to Carlo Ancelotti the need to rebuild at Stamford Bridge is the prime objective for the Russian this summer. While Modric would be a key part of this programme Chelsea will be conscious that his current contract, which expires in 2016, is said to be worth only £40,000 a week, so the offer of a salary of £100,000 or more would prove tempting.

With Liverpool and Manchester United having just paid £18m for Jordan Henderson and Phil Jones, respectively, Modric as an established Premier League and international performer is arguably worth considerably more than the £22m offered by Chelsea and so the west London club can be expected to increase their offer markedly.

Any bid of £30m or more would force Levy into giving serious consideration to allowing the sale, with West Ham United's Scott Parker, of whom Redknapp is a keen admirer, the potential replacement.

That may risk upsetting Redknapp, who recently declared his desire to keep Modric. "We want to keep him here and build a team round Luka," the Spurs manager said. "If you start thinking about selling your best players, you might as well give up. What's the point in carrying on? It effectively sends out all the wrong signals. And, when one player leaves, the rest want to follow him straight out the door. Then you have a situation where the quality of football goes into decline and you're going backwards on the pitch."