However, according to two of Monday’s papers, it will not be on-loan Liverpool striker Andy Carroll who will be their big summer signing.
Both the Sun and the Daily Mail say it is "unlikely" that Sam Allardyce will take up the option to sign Carroll on a permanent basis, forcing the former Newcastle star, who Liverpool paid £35 million for, back to Anfield.
Instead both papers say that the man West Ham really want is Ivory Coast ‘goal machine’ Wilfried Bony.
The 24-year-old plays in the Dutch League with Vitesse Arnhem and has scored 26 goals in 24 games this season - including 10 in his last six.
According to the Sun, West Ham are "close to agreeing a deal that will see Bony complete the season with title-chasing Vitesse before moving to London in the summer."
They say that West Ham will pay around £12m for the striker but the Mail reckons that West Ham may have to cough up £15m if they want to get their man.
Bony is under contract until 2015 but is desperate to move to the Premier League.
He actually wanted to go in January but Vitesse refused to sell as they are battling for a Champions League place.
If the deal does go through it will break the East London club’s current transfer record: the £10.75 million paid to sign Matt Jarvis from Wolves.
Bony would look to command a salary of around £55,000-a-week.
Elsewhere, there is a scary story in the Mirror for Manchester City fans with both Sergio Aguero and Vincent Kompany linked with moves to Barcelona.
However, the paper then goes on to explain that the two players are only back-up plans. The Catalan giants are hoping to extend David Villa's contract and bring in Borussia Dortmund centre-back Mats Hummels and they will only look to the Etihad duo should those deals fall through.
Also in the Mirror is the rumour that Montenegro dangerman Stevan Jovetic could snub a move to Arsenal to stay in Italy.
Both Inter and AC Milan are interested in the Fiorentina striker who is set to play against England on Tuesday night.
Most of the papers lead on preview coverage of that match in Podgorica and in particularly they have been drawn to comments from Juventus striker Mirko Vucinic, who seems to suggest Wayne Rooney is at risk of getting sent off like he did the last time the two sides met.
"There is no doubt that Wayne Rooney is one of the best strikers in the world but we know from the last time England played here that he can sometimes play with a hot head," said Vucinic.
"Our fans will not forget the red card he received and I am sure they will let him know. It is an intimidating place to come and if England want to have any chance then Rooney will need to keep a calm head.
"He is a good player but it has been proved over the years that you can get a reaction out of him. England would have no chance with 10 men and I’m sure their coach will be telling them that."
Back to transfer rumours and Southampton left back Luke Shaw has once again flirted with suitors Chelsea, labelling the Blues his favourite team... after the Saints. (Daily Mail)
Scott Sinclair has emerged as the top target for Southampton after he failed to make an impact at Manchester City. (The Sun)
Chelsea and Manchester City target Edinson Cavani admits he doesn't know where he will be playing next season and says it is up to Napoli whether he stays at the San Paolo. (Daily Mirror)
Manchester United have revived their search for a left-back, creating further uncertainty over the long-term future of Patrice Evra. United scouts watched Porto left-back Alex Sandro in the recent Champions League tie against Malaga and plan to look at others in the position before the season ends. (Daily Mail)
And finally, Chelsea have made an offer for 15-year-old Bursaspor striker Enes Unal. The European champions are understood to have offered a deal worth £1.75m for Unal, who has scored 170 goals in 102 games in the academy league and is expected to represent Turkey in the Under-20 World Cup this summer.
They could face competition for the teenager's signature with Manchester City and United also watching him. (Daily Mail)