The Sun says the London club have shown strong interest in the Ireland Under-21 centre-half.
The 18-year-old is regarded in England as one of the hottest properties outside the Premier League.
Manchester United were tracking his progress last season after he made his first-team debut when still aged only 17. But with United deciding against an immediate move, Collins signed a new deal intended to keep him at Stoke until 2024.
He has further enhanced his reputation this term, making another nine appearances in the Championship to bring his overall total to 12 and his long-term contract has not warded off suitors.