The player in question is Everton's Marouane Fellaini who according to the Mirror sees Arsenal as a "dream transfer" and who has a clause in his contract that means he can leave for a Champions League club for £23 million.
Wenger is a known fan of the 25-year-old Belgian and the funds are there for the Frenchman to spend if he desires with chief executive Ivan Gazidis saying this week: "he is not scared to spend money, but he has to believe he is a getting a top-class player."
The Mirror though says it is the fee that is putting Wenger off making the powerful midfielder his big first signing of the summer.
"Gunners manager Arsene Wenger has made his admiration of the Belgian clear," says the paper, before adding: "However, Wenger is unconvinced that £23m for Fellaini represents good value, and so far has not been prepared to commit to a bid that will trigger his release clause.
"…There is a resignation within Goodison that Fellaini will definitely leave if he is offered a move to the capital - his preferred choice.
"Yet it seems that Wenger's reluctance to loosen Arsenal's purse strings has given the Merseysiders fresh hope of holding onto their star player, despite that get-out clause.
"There is bemusement at Everton about the north Londoners' apparent desire to undercut that release clause and attempt to get Fellaini for less than the stated £23m."
With Everton having spent £15m on Fellaini five years ago – and with £2m in incentives being added since then – they have no intention of selling their prized asset for less than the release clause.
There a juicy rumour in the Daily Mail that Paris Saint-Germain are prepared to outbid Real Madrid in the £85million battle to sign Tottenham star Gareth Bale.
The mega-rich French side have already been linked with Spurs' coach Andre Villas-Boas and if they pull off that move that they hope that Bale might follow.
The paper adds that Bale is happy to stay at Tottenham if he sees them making moves to improve the squad but "will listen to what PSG, Real and Manchester United have to say if Tottenham decide to cash in."
West Ham fans might be excited by a report in the Times which says the club are hoping to bring Manchester United's Wilfried Zaha and Chelsea striker Demba Ba into the club on loan. The Hammers originally wanted Romelu Lukaku from the Blues for a season but it now looks like Jose Mourinho will keep him at the Bridge ahead of Ba.
Fernando Torres could also be one his wait out of Chelsea with Barcelona the surprise latest name to be linked with the £50m flop.
According to the Mirror, Barca are eyeing up a cut-price £17m deal for the striker who they hope would accept the role of "super-sub" at the Spanish champions.
Barcelona are also back on the trail of young Chelsea midfielder Ruben Loftus-Cheek. The 17-year-old impressed the Spanish club's scouts with his performance during the recent friendly with Manchester City in New York. (Daily Mail)
Djibril Cisse is wanted by the Qatari club Al-Gharafa on a permanent basis and the Queens Park Rangers striker will give serious consideration to the proposal. (The Guardian)
Out-of-favour Manchester United winger Nani has his heart set on a move to Juventus or Monaco this summer. The Portuguese international has suffered an inconsistent couple of seasons at Old Trafford and is not in manager David Moyes’s plans. (Daily Mail)
Real Madrid will compete with Chelsea and Manchester City for the Napoli forward Edinson Cavani after the Spanish club held preliminary talks with the Uruguayan's representatives with a view to securing his services before the new season . (The Guardian)
Michael Laudrup's agent, Bayram Tutumlu, has had his ties severed by Swansea amid accusations he has been single-handedly running the club's transfer policy. But both the Swansea manager and Tutumlu insist the agent's departure will have no bearing on Laudrup's future in South Wales. (The Independent)
Finally, Wigan see Steve McClaren and Owen Coyle as the top two candidates to succeed Roberto Martinez and the club hope to make an announcement on Thursday. (Daily Mail)