Current first-choice goalkeeper Guglielmo Vicario is progressing towards a move to Inter Milan in the summer window, leaving Spurs with a decision to make over how they replace him.
It is possible that they stick with Antonin Kinsky if they lose their relegation battle and drop into the Championship.
But if they manage to retain their Premier League status, then a move for Trafford will be explored.
At this moment, Manchester City sources believe a permanent deal could be complicated. While Gianluigi Donnarumma is established as the first-choice stopper at Etihad Stadium, Trafford remains very highly regarded.
It is considered unlikely that City are going to be welcoming of bids for the player, who joined for £27 million last summer from Burnley.
There is a belief among some at City that the 23-year-old keeper could still become their long-term No.1.
However, Trafford has obvious frustrations about a lack of playing time this season and could push for a move elsewhere.
It has been suggested by Flashscore sources that a loan move next season might become an option.
That would be one way to solve the player’s irritation at a lack of regular minutes, while also allowing City to have him as an option to succeed Donnarumma.
Tottenham have been checking out the market over the past six months in terms of searching for new goalkeeping options, but have to put the search on hold for now because of their fight to decide which league they will be playing in next season.