Marca says United were prepared to pay big money for the Norwegian following his performances while on loan at Real Sociedad last season.
But Madrid held off interest from the Old Trafford outfit to bring Odegaard back to the Bernabeu this summer.
It was just the latest effort from United to land the attacker, who first registered an interest in him in 2014, when he was 15.
United then returned for Odegaard last October with Ole Gunnar Solskjaer in charge as the Norwegian was keen to swoop for his young compatriot.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!