Arsenal would reportedly have to come up with an offer of €50m (£42.5m) to convince Real Madrid to sell Martin Odegaard during this summer's transfer window.
The Norway international spent the second half of last season on loan with the Gunners, making 20 appearances in all competitions, contributing two goals and two assists in the process.
Arsenal are said to be keen to re-sign the 22-year-old this summer, but a loan deal is thought to be unlikely due to Real Madrid's financial issues.
According to ESPN, Los Blancos are confident that Odegaard will be an important player for the club, but an offer in the region of €50m (£42.5m) would be seriously considered by Carlo Ancelotti's side.
The Norwegian has only made 11 first-team appearances for Real Madrid since arriving in 2015, spending time out on loan with Heerenveen, Vitesse, Real Sociedad and Arsenal.
The Gunners are also believed to be considering a move for Leicester City's James Maddison, although the Foxes are said to value the England international in excess of £70m.
