The 30-year-old, who had a loan spell with the Red Devils last season, is a free agent after leaving Brentford by mutual consent last week.
"Paul is well known to Crawley fans. He's been here before and because he's out of contract we can sign him if we wanted to," Gregory told BBC Sussex.
"He's a clever, experienced player and that was the reason I asked him to come back. We'll make a decision at the end of the week. We're delighted he's decided to come back here for a few days."
Hayes scored two goals in 11 appearances during his loan spell at Crawley.