Maurizio Sarri’s Blues are desperately struggling for goals this season, with just 40 in 24 Premier League games this term – at least eight fewer than any other side in the top six.
They have moved to solve their problems by signing Gonzalo Higuain but the Argentine is yet to score and has been withdrawn early by Sarri in each of his two appearances so far.
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And Gallas thinks they should be doing all they can to convince Griezmann to ditch Atletico Madrid for Stamford Bridge.
“Griezmann is one of the top five strikers in the world,” the ex-Blues defender said.
“With his quality, I’m sure he can damage a lot of defenders. I would love to see him in the Premier League.
“He’s a very patient, diligent player who scores goals consistently. He would be perfect for Chelsea.”
Griezmann might be an unrealistic target at the moment but it could be a busy transfer deadline day at Chelsea elsewhere.
Boss Sarri is understood to be desperate for a new midfielder to replace Cesc Fabregas, who joined Monaco earlier this month.
They missed out on top target Nicolo Barella after he decided to stay at Cagliari, while Leandro Paredes has moved to Paris Saint-Germain from Zenit Saint Petersburg.
Reports claim they will now make a late bid to sign Abdoulaye Doucoure from Watford.
The in-demand Frenchman has attracted interest from all over Europe after his impressive displays this season and Sarri is said to be a big fan.
Chelsea also face the prospect of losing some of their own players on deadline day, with the future of Callum Hudson-Odoi still uncertain.
The 18-year-old winger has been the subject of four offers from Bayern Munich and submitted a transfer request in a bid to force through a move.
Hudson-Odoi has been told that he is staying but whether they can keep him at the club beyond the 11pm, deadline remains to be seen.
The Blues are also bracing themselves for a bid from PSG for Willian.
The French giants need cover for the injured Neymar and have reportedly made signing his Brazil team-mate their priority.