However he also has pressing concerns within his own squad as rival clubs circle looking to take Wayne Rooney from their grasp.
With the new season approaching and plenty of transfer business still to conclude, Moyes will be hoping to significantly strenghten an area of his first team that has long been under the spotlight.
But is it worth acquiring Fabregas if it means losing the talismanic Rooney?
Moyes said after the 3-2 friendly loss to Yokohama F Marinos: "As far as we know, he [Rooney]'s coming on. He's started light jogging and the feedback we're getting from the physios is that he's progressing. We've said and the club have said he's not for sale. That's not changed."
So should Moyes sacrifice the 27-year-old in favour of snapping up former Arsenal star Fabregas? Or can the current squad continue to move forward without addressing the gaps in central midfield?