Moyes is yet to make a senior signing since his appointment.
But he told PA Sport: "That is not something Manchester United are frightened of. Manchester United are more than happy to compete with all of the teams. There has been a change in the dynamic because of PSG coming on the scene recently. That has altered things. But Manchester United will always compete.
"One thing it has got is the history. It has got the name. It has got the success. Players do want to be connected to that and one day say they have played for Manchester United. That is a big pull for any player."