According to The Sun, the Eagles will launch a fresh move for the midfielder having made enquiries into re-signing him last summer, while the Metro claims that the England international is currently valued at £30m by his boyhood club.
Vieira is understandably keen to reunite with the 22-year-old after his starring performances on loan at Selhurst Park last season, with Gallagher notching eight goals and three assists in 34 Premier League appearances, averaging a 7.09 rating from WhoScored for his performances.
This campaign has been a disappointing one for the young midfielder at Stamford Bridge, as he has managed just one goal and one assist in 17 league appearances, earning a far-less-impressive 6.53 rating from WhoScored.
The report from The Sun claims that Gallagher is still committed to making it at Chelsea but if Graham Potter brings in more midfielders under the free-spending Todd Boehly, then the academy graduate might find his opportunities limited and could look to rediscover his best form at Selhurst Park.
Vieira was full of praise for the Englishman last season after he scored twice in a 3-1 win over Everton.
“Conor has this passion for the game when he is on the field like a Ray Parlour, but I would say he has maybe the quality finishing of a Frank Lampard.
“It is a manager’s dream to have a player like Conor because when he is on the field, he will give everything.”
The French manager undoubtedly needs another all-round midfield option to play alongside Cheick Doucoure at Palace, with Will Hughes having sadly failed to cut it since his arrival from Watford in the summer of 2021.
The former Derby County man has made just 35 appearances since then, contributing one goal and one assist, while he has been limited to just 129 minutes of action in the Premier League so far this campaign.
Considering the different impacts the two midfielders have had in their time at Palace, it seems clear who Vieira would prefer to have in his side and adding Gallagher this month would surely allow the French manager to get rid of Hughes for good.