The Sun says the England youth international is wanted by both Premier League giants.
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Tyjon has resisted Rovers' attempts to secure him to a pro contract ever since turning 17 years of age.
Arsenal had multiple offers rising to £1m over the summer rejected by Rovers and remain keen this month.
United are also interested and are attempting to secure Tyjon's signature.
With his scholarship deal to expire this summer, January is the final chance for Rovers to get a decent development fee from Tyjon's sale.