The 25-year-old has told officials at the Santiago Bernabeu that he wants to leave Spain at the end of the season, after falling down Jose Mourinho's first-team pecking order, and has set his sights on a move to the Premier League.
Spurs boss Andre Villas-Boas has been credited with an interest in bringing Higuain to White Hart Lane, with the Portuguese desperate to add another striker to provide competition for Jermain Defoe and Emmanuel Adebayor.
Tottenham are understood to have a strong relationship with Real Madrid, after allowing Luka Modric to join the Primera Division giants last summer.
Higuain could be included in any deal that sees Gareth Bale move to the Spanish capital, but Villas-Boas is determined to retain the services of the Welsh winger for at least one more season, particularly if Spurs can qualify for the Champions League this year.
If, as expected, Tottenham press ahead with a bid to lure the Argentine international, they are likely to face competition for his signature from north London rivals Arsenal.
Gunners chiefs have reportedly approached Higuain's representatives to let them know of Arsene Wenger's interest in taking the former River Plate star to the Emirates Stadium.
Real Madrid will hold out for around £22million, after giving the player permission to start negotiating a move away from La Liga, but it remains to be seen whether Arsenal or Tottenham will be willing to meet that valuation when the transfer window reopens in the summer.