Press Association Sport understands Spurs tested the water with a bid on Tuesday evening which came nowhere near meeting the Magpies' valuation.
However, it is understood that the Tyneside club will sell the 27-year-old to the Londoners if they can come up with £30million, and that they will accept the fee in five instalments of £6million apiece.
Sissoko, who is on international duty with France, has given permission to leave the camp to tie up a move, but as yet no agreement between the two clubs is in place.
Newcastle initially put a £35million price-tag on the 27-year-old former Toulouse player, who shone for the hosts at the Euro 2016 finals, in the wake of relegation in a bid to ward off time-wasters.
Sissoko has been agitating for a move away from St James' Park all summer, repeatedly speaking of his desire to play Champions League football, and he has been linked with a series of clubs including Real Madrid, Juventus and Borussia Dortmund.
His employers have been less than impressed by his come-and-get-me pleas, following a season during which he showed his best form only as Rafael Benitez attempted, ultimately unsuccessfully, to drag Newcastle out of a relegation tailspin.
Sissoko has not kicked a ball for the club during the new campaign, but with owner Mike Ashley having no need to sell, his future remains uncertain.
Big names Andros Townsend, Georginio Wijnaldum and Daryl Janmaat have all left Tyneside this summer, the Dutchmen at sizeable profits as Benitez has re-built his squad for life in the Sky Bet Championship.