The Ivory Coast international attacker joined the Gunners for £72 million ($89m) in the summer from Lille, having been given a big billing following a highly impressive season in France that saw him score 22 goals and lay on 11 assists.
His start to life in England has been relatively slow, and though he netted from the penalty spot in the 3-2 win over Aston Villa, the rise of Bukayo Saka has seen the academy prospect win plaudits and push for more regular football.
Keane, it seems, would be among those, having told Sky Sports in the aftermath of Arsenal’s 1-1 draw with Manchester United at Old Trafford on Monday: "I’ve been disappointed since he’s come to the club.
"His body language isn’t great, and we make excuses for players a lot, like it takes time to settle into a club, but Pepe for the money they’ve paid needs to do a lot more.
"His poor work rate, his lack of quality and end product, and again his body language, he doesn’t seem up for the fight."
He was rather more effusive with praise when considering another new arrival, though this time one at Old Trafford.
Daniel James has won an increasing fan club for his performances since arriving at the Red Devils from Swansea City in the summer, and Keane is another to be impressed by the young Welshman’s contribution to date.
"He’s been a big plus for them, considering when they signed him in the summer they thought he might be in the background, learning his trade," he said.
"He’s their biggest threat, you think something’s going to happen with him. And he’s still new to the game, he’s learning. He’s going at people, he’s exciting, but maybe his end product needs to improve, and it will the more games he gets."
Despite United’s tough start to the season, manager Ole Gunnar Solskjaer retains the backing of the former Republic of Ireland international, who spent 12 years at the club where he remains an icon after making 480 appearances and helping them to the treble in 1999.