Chelsea's stubborn pursuit of Luka Modric is set to continue with Tottenham Hotspur braced to receive a third improved offer in excess of £30m for the unsettled Croatia international.

Modric, who is contracted to Spurs until 2016 and is on tour with the club in South Africa, has publicly expressed his desire to move to Stamford Bridge and, with his relationship with the Tottenham chairman, Daniel Levy, having apparently fractured beyond repair, had submitted a formal transfer request on the eve of the squad's departure for Johannesburg. Levy maintains that the player will not be sold at any price.

Yet Chelsea have been suitably encouraged by Modric's clearly expressed desire to move to Stamford Bridge - "They are a club all players dream of joining," he told the Croatian newspaper Sportske Novosti last weekend – that they will maintain their interest in the midfielder. The Londoners have backed off in the past in their pursuit of a player when warned there was no desire to sell, most notably when Santos refused to countenance the young striker Neymar's transfer last summer, but they intend to continue to test Tottenham's resolve to retain the 25-year-old and will lodge a third bid.

There is an acceptance that theirs is likely to prove a protracted and acrimonious chase that could drag well into August, though Modric has been identified as Chelsea's principal target and will remain a priority. Their previous inquiries – an opening offer of £22m was rejected last month, with an improved package worth around £27m knocked back early last week – had served to infuriate Levy and strengthen his resolve to retain the player.

The Spurs manager, Harry Redknapp, has since stressed: "We know Luka wants to leave, so whether he writes it down on a piece of paper doesn't really make any different to our stance." Modric, who has been suffering from a slight ankle injury, is expected to miss Tottenham's friendly on Saturday against Kaizer Chiefs at the Peter Mokaba Stadium, Polokwane.

Chelsea, whose first team depart on a two-week tour of the Far East on Sunday, remain in dialogue with Anderlecht over the potential signing of their Belgium international forward, Romelu Lukaku, though the clubs are still some distance apart in terms of their valuation of the teenage striker.

The Londoners are also considering whether their interest in the England midfielder Scott Parker should be pursued, with West Ham United having now indicated they would allow the player to depart Upton Park only in a permanent £8m move rather than on a season-long loan.

A temporary switch, even involving the payment of a substantial loan fee, had made some financial sense to Chelsea given the loss of Michael Essien to a serious knee injury until February at the earliest. Parker, too, would have favoured that arrangement though Aston Villa have since expressed an interest in signing the 30-year-old on a permanent basis and may yet meet West Ham's asking price.

Villas-Boas did make some progress on Friday by agreeing new contracts with the highly rated England Under-21 internationals Josh McEachran and Ryan Bertrand. The former has signed a new five-year deal initially worth around £25,000 a week having impressed when given the chance to feature in the first team last season. The 18-year-old should play some part in Saturday's friendly at Portsmouth.

"This season my target is just to play more minutes," said McEachran, who played 17 times under Carlo Ancelotti. "If not at Chelsea, then I will go out on loan, but I want to play here as much as I can."

Bertrand, who was an ever-present for Stuart Pearce's Under-21s in the summer's European Championship in Denmark, has signed a four-year deal and, with competition fierce at left-back, could now be made available for loan.

Newly promoted Swansea City had expressed some tentative interest in bringing the 21-year-old, who spent the first half of last season at Nottingham Forest, to the Liberty Stadium.