The Lilywhites are understood to be long-term admirers of the England international, whose career at Goodison Park is currently in limbo following an ultimatum made by boss Ronald Koeman.
Barkley was warned to either sign an extension to the contract that runs out next summer, or instead be sold to the highest bidder should his valuation be met.
Despite rumoured recent interest from Premier League champions Chelsea, however, the Toffees have yet to receive any formal offers for the 23-year-old.
That will likely remain the case, according to the London Evening Standard, as Spurs are expected to delay opening talks until they know the full extent of the player's ongoing hamstring injury layoff.
Barkley has yet to feature this season due to the problem and, despite facing potential competition from rivals Chelsea, it is claimed that Tottenham are prepared to take a step back and wait until 2018 before sealing a transfer.