The Frenchman, who has featured in just three senior games for the English champions, has been linked with a move to Scotland recently.
Manchester City have a history of doing business with Celtic and it was suggested that Gomes could be the latest piece of business between the two sides.
However, there is no truth to those links, with the club being content with their business so far this summer and not plotting a move for Gomes.
Celtic manager Ange Postecoglou is still keen on adding to his ranks, though the Hoops are nowhere close to finalising any deals.
The Scottish champions are expected to be in the market for a striker if they manage to successfully offload former West Ham man Albian Ajeti.
The Swiss striker would be able to leave Celtic Park if the right deal is offered.
Gomes meanwhile has had two spells away from Manchester City on loan, at PSV Eindhoven and Barnsley.
