But United have also been linked with a move for Thiago Alcantara, with Bayern Munich demanding a €30 million (£27.6m) transfer fee for the Spain international.
United, however, have been put off by the midfielder’s wage demands, which are in excess of £200,000 a week.
According to The Sun, United have now turned their attention to Valencia’s central midfielder Racic.
The 22-year-old has made just two appearances for the Spanish club and has spent the last two season on loan at Tenerife and then at Portuguese side Famalicao.
Racic has a £92m release clause in his deal with Valencia but The Sun reports that a bid of £28m from United could be enough to sign him.
The Serb, who is yet to by capped by the senior side, stands at 6ft 4in and offers a powerful presence in midfield.
United have been keeping tabs on Racic’s performances and the 22-year-old could provide competition for Nemanja Matic in Solskjaer’s midfield.
United could now turn to a loan deal for Gareth Bale, with Real Madrid keen for the Wales international to leave the club.
Reports have suggested that Bale would be open to joining United, although the 31-year-old’s £600,000-a-week salary could prove to be a stumbling block as Madrid would need to fund part of his wages.