The reports in Spain suggest Rafa Benitez is weighing up a €30m bid for the Argentina forward, but may have to wait until the summer to land the striker.
AS claim Roman Abramovich is keen to fund a move for a big-name striker this season, and the name of Higuain has emerged as a potential target.
The European champions have been strongly linked with Atletico Madrid striker Radamel Falcao, but it now seems as though the Colombian international will stay at the Vicente Calderon, at least until the end of the season.
Benitez sanctioned the sale of Danny Sturridge to Liverpool for £12m this week, leaving Fernando Torres as the club's sole recognised striker.
The Blues have been linked with a move for Newcastle forward Demba Ba, but the Senegalese frontman is relatively cheap at £7m and his injury record suggests the deal is more than likely to be a short-term measure.
That could free Chelsea up to move for a big-name in the summer. Higuain has fallen out of favour at the Bernabeu, with Real Madrid boss Jose Mourinho preferring Karim Benzema, flanked by Angel Di Maria and Cristiano Ronaldo.
Chelsea slipped to a 1-0 defeat to Queens Park Rangers last night - former-Blues winger Shaun Wright-Phillips grabbing the only goal of the game - and the match highlighted the team's need for more forward options.
The result leaves Chelsea seven points behind Manchester City, and 14 points behind league leaders Manchester United. The Stamford Bridge side travel to Southampton next, to take on Nigel Adkins's side in the FA Cup third round.