Walcott’s future at the Emirates Stadium has been called into question after Arsenal completed the £52 million signing of Alexandre Lacazette on Wednesday.
The 28-year-old fell down the pecking order in Arsene Wenger’s side at the back end of last season and his route to the first team is now further blocked by the club’s record signing.
Winterburn, who represented the Gunners and the Hammers, believes the England international should consider a move to the London Stadium where he would be an ideal fit for Slaven Bilic to play alongside countryman Carroll.
“The problem for Theo is that Arsenal switched the system at the end of last season and that system doesn’t suit him, not at Arsenal anyway,” Winterburn told bwin. “Theo will think that if Arsenal are trying to limit his game time, he’ll feel like ‘where do I fit in? Is it time for a new challenge?’
“I think when players of that quality become available, it’s natural to say that they would say they are interested.
“West Ham playing with two up front including Carroll with Theo, I can see that working very well. Then you also have the option of playing him off the striker or playing right or left, so you’re getting a fair bit for your money.
“The problem for Theo at Arsenal is where do they see him playing if they stick to a back three or back five?”
Both parties would benefit if Walcott joined West Ham
The 28-year-old did actually enjoy a fine season in front of goal during the 2016/17 campaign as only Alexis Sanchez (30) netted more than his 19 goals across all competitions – including efforts against Liverpool, Chelsea, Manchester City and Bayern Munich.
However, he lost his place in the side following Arsene Wenger’s decision to switch to a 3-4-2-1 formation in mid-April – making four appearances from that point – and was an unused substitute in the FA Cup final victory over the Blues.
A pacy forward, capable of playing through the middle or on the right-flank, Walcott netted 10 times in the top flight of English football last term – including one in the 3-0 win over the east London outfit – and weighed in with two assists.