Moyes is considering signing the 26-year-old in a emergency loan move as he has a limited budget for new players.
Quaresma is out of favour at Inter Milan and is keen on regular first-team action.
Quaresma joined Inter for £16million in 2008 and the Italian side are looking to recoup around £8million by selling him next summer.
Everton, Paris Saint Germain and Napoli are all reported to be interested in the winger, according to The Mirror.
