Arsene Wenger's side have endured another frustrating season at the Emirates Stadium, compounded in the last seven days by emphatic home defeats to Manchester United and Chelsea.
They have now completed four campaigns without picking up a trophy since their 2005 FA Cup triumph at the Millennium Stadium.
But despite the 25-year-old scoring 16 goals in 37 appearances in 2008/09 - and being one of the club's more senior players at a time when supporters are crying out for the North London outfit to invest in experience - Dixon believes the former Monaco man should move on.
“The team could do with a new striker,” Dixon - who made more than 450 league appearances for Arsenal - said in The Times.
“Like a lot of people, I was disappointed with Emmanuel Adebayor in the [Champions League] semi-final. He has a great physique and terrific talent and should be a real handful.
“But at this level, week-in-week-out, he doesn’t have the right attitude. He’s not like a Carlos Tevez or Wayne Rooney, who compete all the time in every game they play.
“He hasn’t got that, and to me, he hasn’t got what it takes to compete at this level. You can’t turn it on when you feel like it.
“If Milan come in for him, I would let him go, then use the money to strengthen other areas.”
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