The marksman is without a club after leaving Everton at the end of his contract following a nine-year stint.
His past few seasons have been marred by injuries and he was limited to 19 Premier League starts last campaign, scoring three goals.
But Ruben Amorim sees him as a useful cut-price option as Man United seek to stay on the right side of financial rules, according to The Sun.
United have already added Matheus Cunha from Wolves for £62.5million and Paraguayan teenage sensation Diego Leon for £7m from Cerro Porteno to their squad.