Sissoko has emerged as a shock target for Real after playing a starring role for France at the European Championships, particularly in their semi-final victory over Germany and defeat to Portugal in the final.
Real believe they will be able to sign the 26-year-old, who has been infuriatingly inconsistent during his three-and-a-half years on Tyneside, for around £30m, a huge saving on the £100m Manchester United are set to splash out on Pogba.
That deal should be concluded in the next couple of weeks and, following preliminary talks, Newcastle believe Real will make a bid for Sissoko once it is certain Juventus have agreed to allow Pogba to return to Manchester United.
The Spanish giants had also hoped to sign Pogba this summer, but were forced to accept they do not have the financial power to outbid the English club on this occasion.
As a result, although Sissoko’s form at club level has often left a lot to be desired, they are willing to gamble on the former Toulouse player on the basis of a few eye-catching displays for his country.
Interestingly, although Pogba was the poster boy of France’s Euro campaign, it was Sissoko who shone alongside him in midfield, particularly against the Portuguese.
Sissoko’s talent has never been in doubt, but his motivation and commitment have often been questioned at Newcastle, who were resigned to losing the player as soon as they failed to avoid relegation to the Championship back in May.
Newcastle had been looking to sell Sissoko for around £22m, but raised the asking price in the aftermath of his excellent displays for Les Bleus.
That initially sparked resentment in the Sissoko camp, as they feared he was being priced out of a move, but they are now also confident the interest from Madrid is strong enough for them to match Newcastle’s new valuation.
West Bromwich Albion were the only club to express a firm interest in signing Sissoko before the tournament, but there have been plenty of enquiries since, with Borussia Dortmund, Juventus and Everton also understood to have shown an interest in signing a player who has three years left on his contract at St James’ Park.
Newcastle supporters will be stunned if Sissoko leaves for Madrid, given the standard of his performances for them, but sources have told Telegraph Sport that manager Rafa Benitez insists the interest from his former club is genuine.
Remarkably, if the Sissoko deal goes through, Newcastle will have recouped around £60m from player sales this summer, after Andros Townsend moved to Crystal Palace for £13m last month and Georginio Wijnaldum joined Liverpool for £25m last week.
Benitez will be allowed to reinvest the money in new players and still wants to sign a centre forward, a midfielder, a left winger and a left back before the close of the transfer window at the end of August.