The duo have both been linked with exits from the Emirates this summer.
The duo have both been linked with exits from the club in the summer transfer window, with suggestions Arsene Wenger may look to sell several stars.
Oxlade-Chamberlain in particular looks destined to leave, having failed to develop as many had anticipated when he was a hot prospect at Southampton.
Much of that has been to do with injuries curtailing his game time, although a serious competition for places at the club has also played its part.
And Thompson believes that both he and Arsenal teammate Walcott should look to leave for the good of their careers.
“Theo Walcott and Alex Oxlade-Chamberlain, if they want to further their careers they need to move,” he told Soccer Saturday.
“If they want more football, they need to move. Technically, I think the two are just lacking in what Arsene Wenger wants.
“The way they’ve been over the last two years, I think they need to further their careers. They seem like they want to play football and they wont do that at Arsenal.”
Should Arsenal decide to sell both players, there is no denying that there would likely be several clubs interested in both.
Despite struggling at Arsenal, they are both quality players on their day, as they have shown for both club and country on occasion, and they could improve many teams considerably.
Whether the Gunners can find buyers though remains to be seen, with both players likely to be on wage packets that other clubs would struggle to match.