David Moyes fears Leighton Baines and Luke Shaw may be out of reach in the January transfer window, with the Manchester United manager aware that Everton and Southampton are unwilling to sell their respective left-backs.

Moyes remains keen to bring in a player to offer competition to Patrice Evra, yet Everton, after their refusal to sell Baines to their former manager in the summer, are determined to maintain that stance.

At the weekend Everton's manager, Roberto Martínez, signalled the club's intent to keep Baines. "In football you don't work long-term, you go window to window, and I can guarantee that Leighton will be here at the end of the season. That is 100%," he said. "That is how you work from window to window – to have a stronger squad than previously. Leighton is vital for us in the second half of the season. Bryan Oviedo has been terrific but we need Leighton and Bryan fit for us if we are going to fight for our football dream."

While Baines turned 29 earlier in the month, Shaw is only 18, so would represent a longer-term investment for United. However, Mauricio Pochettino, the Southampton manager, is adamant the teenager will not be sold during the winter window.

Moyes may still decide to test the resolve of Everton or Southampton with a bid. Yet with regard to Baines, when United finally made a £15m bid for him on the last day of the summer window, having previously made combined offers along with his team-mate Marouane Fellaini, the Goodison club rejected the move. Baines still might have become a United player if he had tried to force any transfer by informing Everton he wanted to leave or by allowing this stance to become public. But his failure to do so, plus Everton's insistence he will not be sold, has hardened Moyes's view that it will be particularly difficult to prise away the left-back in January.

United pressed ahead with the joint-bid strategy, believing that if separate offers had been made Everton would have accepted the one for Fellaini, with the monies received allowing them to turn down any approach for Baines.

Shaw, who is a Southampton fan, signed a five-year deal last summer, stating then that he would be at the club for the duration of that contract.

Last week Pochettino said: "The player wants to stay at the club. He has made a statement about this himself. Other clubs can watch him and show their interest but he does not want to go anywhere and we do not want to sell him."

Beyond a left-back, Moyes will continue to search for a midfielder, although he recognises the difficulty of making the right calibre of signing in the mid-season window.