The 34-year-old defender is out of favour at the Santiago Bernabeu after missing much of last season with a back injury and manager Jose Mourinho will use him to entice Spurs into selling Modric.
New White Hart Lane chief Andre Villas-Boas is resigned to losing the Croatian playmaker this summer after he professing his wish to join the Spanish champions.
Chairman Daniel Levy rebuffed three bids by Chelsea last year but is now willing to part with the 26-year-old who has made it clear he wants to play under Mourinho at Madrid.
However Los Blancos are unwilling to meet Levy’s £35 million valuation of Modric and are hoping to land him for £28m by making Carvalho part of the deal.
The earlier plan to include Nuri Sahin in a like-for-like swap was ended by the Turkey midfielder after he refused a move to North London despite struggling for first team football last term.
Chelsea are still in the hunt for Modric but Madrid are confident of landing him and seeing off the Champions League winners’ interest having done so already with Manchester United.
Meanwhile, Emmanuel Adebayor is close to becoming Villas-Boas third signing since taking over from Harry Redknapp following Gylfi Sigurdsson and Jan Vertonghen.
The Manchester City striker spent last season on loan at Spurs scoring 17 times and the Portuguese tactician sees him as the perfect spearhead for his preferred 4-3-3 formation.
A £5m fee has been mooted whilst the club will offer Adebayor a significant signing-on-fee that will compensate for having to offer him lower salary than the £180,000-a-week he was on at City.
Villas-Boas is also monitoring Internacional striker Leandro Damião as he looks to boost his attacking options.