Both teams are said to be keen on adding to their attacking ranks in the summer, and could make a move for Higuain, who hinted his future may lie away from the Bernabeu.
The Argentinian told Spanish newspaper Marca over the weekend when asked about his future: "I'm not going to talk about that now."
"I can only say that I'm committed to the club and will help the team until the end of the season."
Higuain offered a glimpse of his class on Saturday, scoring a superb goal in Madrid's 5-1 win over Celta Vigo.
Should Higuain decide to leave Madrid, the Express claim that both Arsenal and Tottenham are the front runners for his signature. The striker's father revealed he would view a move to the Premier League as "a great opportunity" last year amidst reported interest from Manchester City
Los Blancos have been heavily linked with a move for Spurs star Gareth Bale, who has enjoyed his finest season to date at White Hart Lane.
The forward has scored 17 Premier League goals and helped his side reach the Europa League quarter-finals - although an ankle injury against Basel has impeded his progress and put Spurs' in danger of exiting the competition after a 2-2 draw in the first leg last week.
Reports last week suggested Madrid could be ready to offer Higuain as part of a deal to land Bale in order to lower his asking price.
However Arsenal may make a move to hijack a deal for Higuain as they look to add to their squad over the summer. Recent reports suggest Gunners boss Arsene Wenger will get the green light to spend big if he guides his side to Champions League qualification at the expense of Spurs, and a striker is said to be top of his transfer hit-list.