The forward scored a hat-trick against Arsenal on Saturday to boost his chances.
The giant forward was in fine form on Saturday afternoon as he scored his second ever career hat-trick in a 3-3 draw with rivals Arsenal.
It was a typical Carroll performance as he powered home two headers in a game that saw him terrorise the Gunners back line.
There is much debate about whether he should be a part of Roy Hodgson’s squad in France given he offers something different to what is available at present.
And Lennon says he would have him in the 23 man group were he the Three Lions boss.
"I would (take him) yes,” he told BBC Sport.
“He's my type of centre-forward. He looks really mobile, he's chased one down the line with Koscielny, who's quite quick and he's actually beat him in a foot race.”
"With 10 minutes to go in an England game, he could be an option for Roy Hodgson."
The problem for Carroll is that he is fighting for a spot in the squad when England’s striking options are at their best in a long time.
Harry Kane and Jamie Vardy have both shone in the Premier League this season; while Wayne Rooney is unlikely to miss out given he is captain.
If Hodgson decides to take five strikers that leaves just two places, with Carroll, competing with Hodgson favourites Daniel Sturridge and Danny Welbeck for one of them.