The two Premier League clubs were believed to be in a tug of war for the young midfielder in January.
The 20-year-old is enjoying a breakout season at Lille, helping the club to a current fourth-place standing in Ligue 1.
Soumare has been compared to the likes of Paul Pogba because of his multi-faceted play in the middle of the park.
Reports suggested that Soumare was very close to leaving during the winter transfer window and it seems his head has been turned.
Galtier has stated that there is plenty going on behind the scenes between the club and his player.
"There is a situation at the club that I do not comment on," he told L'Equipe.
"In seasons, there can be tension between a player and his club. We'll settle this internally and find a solution."
The coach was responding to his decision to leave Soumare out of the matchday squad that faced Marseille on the weekend.
Manchester United could be looking for a Pogba replacement come summer amid speculation surrounding the Frenchman's future.
Meanwhile, Chelsea are believed to be fearing a similar fate will befall them with regards to N'Golo Kante.
Soumare's abilities are understood to fit both moulds, hence the heavy links to both clubs.
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