Reports in France claim United offered Tottenham close to 150million euros (?125million) for the winger, who joined Real Madrid for 100million euros.
Speaking after his side's 2-0 victory over Crystal Palace, Moyes told BT Sport that now the transfer window had shut he would not be commenting on such a matter.
However he added: "I have said many times we are always bidding for the best players."
Speaking on Friday, Real Madrid coach Carlo Ancelotti said: "I know that Tottenham received a higher bid for Gareth Bale than the one from Real Madrid."
And French newspaper L'Equipe claimed that bid came from Manchester United, but Bale personally insisted on joining Real Madrid.