The England international has impressed during a loan spell at Barcelona, rediscovering his form under manager Hansi Flick and emerging as an important figure in the Spanish club's attack.
Despite his positive impact, Blaugaran are believed to be reluctant to activate the £26 million option to make the deal permanent due to ongoing financial constraints.
The uncertainty surrounding his future has alerted a number of top European clubs, including Arsenal, Chelsea and Bayern Munich.
According to Daily Mail, Rashford's representatives believe Arsenal could enter the race if the financial terms are favourable.
The Gunners are expected to be active in the transfer market after falling short in major competitions, with Arteta keen to add proven quality to his squad.