The teenage forward, who can also play at left-back, has been a long-term target for the north Londoners.
Sessegnon is out of contract next summer and does not intend to sign a new deal at Craven Cottage.
However, Fulham are adamant that they will not sell the England Under-21 international for less than £40m.
Tottenham are remaining patient in their bid to sign the youngster, with Mauricio Pochettino required to sell some fringe members of his squad in order to raise funds.
Spurs broke their transfer record by acquiring Tanguy Ndombelefrom Lyon for £55m last week.