The Blues missed out on signing the Nigerian international despite making a late push for the striker as he neared the exit at Napoli.
However, the former Liverpool player is backing the Stamford Bridge giants to revive their pursuit of the former African Player of the Year, who is in excellent form for Galatasaray.
“He (Osimhen) would change things for Chelsea without a shout of a doubt. He knows how to put the ball in the back of the net. His numbers are flying in, his numbers are great,” Pennant told Talk Sports.
“I’m gonna look back to Jackson and how many chances he gets a game, but the conversion rate isn’t great. He can have three or four clear-cut chances and he won’t put any of them away.
“You’re scratching your head, thinking about how have Chelsea come away with a draw or a loss. I think someone like Osimhen, who is prolific in front of goal would boost Chelsea or boost any team.”
Osimhen turned down a lucrative move to the Saudi Pro League after Al-Ahli had an €80 million (£68m/$88m) offer accepted, ultimately agreeing to a season-long loan in Turkey.