The latest to be heavily linked with a move to East London is England international Walcott, as reported by the likes of the Daily Mail.
According to reports, West Ham will offer Walcott regular first-team football in a bid to lure him from the Gunners.
If the reports are true it begs the question why and based on what evidence is Walcott A) worth "big money" and B) would he even get in the Hammers side?
Slaven Bilic's East London revolution
With the plaudits and the club's impending move to the 60,000 seater Olympic Stadium looming large this summer has come the inevitable headlines and speculation.
Great move for Theo, but not for West Ham
West Ham would be a fantastic move for the 27-year-old winger.
But would Walcott be such a good move for the Hammers?
The injury-prone star has played just 231 games in 10 years at Arsenal, that's just 23 games a season. And Arsenal's season usually comprise of around 55 matches all told.
In that time his goal record is hardly outstanding with 55 strikes giving him a ratio of less than one in four.
Yes he has electric pace, but a decade on from his huge move from Southampton to North London, where he has played under one of the finest managers in world football, we are still none the wiser of his best position.
He won't budge the 'beast'
You could even argue with Michail Antonio performing brilliantly in his debut season on the right wing and coming runner-up in the prestigious Hammer of the Year awards, would Walcott even get in the team?
Walcott certainly would not dislodge the powerful, explosive former Nottingham Forest star easily and would West Ham really play him up front?
If the Hammers do take a gamble on Walcott, they would be abandoning the transfer policy which has served them so well in recent years, a transfer policy which was very deliberately and radically changed towards the end of Sam Allardyce's tenure.
Co-owners David Sullivan and David Gold brought in talent spotter Tony Henry two years ago and the club's transfer business ever since has been some of the best in its history.
Dimitri Payet arrived for just £10 million, Manuel Lanzini for even less, Cheikhou Kouyate cost just £7m, Aaron Cresswell just £3m, Diafra Sakho the same.
Move would abandon transfer principles
They have also brought in prodigious young talents like Martin Samuelsen, Sam Byram and Tony Martinez from Valencia with a view to the future.
West Ham used to be a club that offered a last pay day to injury-prone players who had seen better days but the last two years have changed all that.
Why risk spoiling all the progress over the last few years for Theo Walcott... it just doesn't add up.