Grecians Chairman Ivor Doble told the Exeter Express & Echo: "If someone is interested in him then we've got to talk to them, that's obvious.
"It's about four clubs that are interested and he's said he wants to go to a higher club."
The former Cardiff frontman spent a short trial spell at Stoke in December, but they haven't followed up their interest.
1st Division outfit Birmingham City are rumoured to be keen on signing him, while Hull City and their Division 3 rivals Luton Town and Mansfield Town are also showing interest. He is thought to be valued at around £150,000. A move to Boothferry Park would see him linking up with former Exeter strike-partner Gary Alexander.
Roberts' name has been in the referee's notebook more times than it has been on the scoresheet. So far this season he has been sent off once and booked 9 times, equalling his total bookings for last year.