Arsenal decided to sell Martinez last summer after his impressive spell between the sticks in the absence of Bernd Leno.
The Argentine went on to be hugely impressive at Aston Villa last season and has firmly established himself as the number one both for his club and for Argentina, with whom he won the Copa America.
Arsenal are close to spending more than they received for Martinez to sign Aaron Ramsdale from Sheffield United this summer.
Keown stressed that the Argentine should still be at Arsenal, and claimed the club offered the goalkeeper a contract that he was never going to sign.
He stressed that Martinez wanted to be Arsenal number one, but the wages on offer from the Gunners did not match his ambition.
The former defender said on talkSPORT: “Martinez should be still at Arsenal Football Club, he shouldn’t be playing for Aston Villa.
“And now he is the number one goalkeeper for Argentina.
“He didn’t want to go.
“I believe he was kind of offered a contract that he was never going to sign because he wasn’t really given the position.
“If you want to make him the number one, give him number one wages.”
It is unclear whether Ramsdale is being brought in to replace Leno or to push the German for a place between the sticks.