The Toffees legend opted to leave the club when his contract expired in June and the veteran defender is keen to keep playing for at least another season.
David Moyes had confirmed Coleman was offered a coaching role at Everton, but he accepted the 37-year-old's desire not to hang up his boots just yet, as he wants to remain involved with the Republic of Ireland squad heading towards UEFA Euro 2028 qualification.
Coleman reportedly wanted to stay in the Premier League, but no offers have arrived as yet, as he weighs up a move to Bramall Lane after setting an EPL appearance record for Everton (374).
Reports from the Sheffield Star claim 'exploratory contact' has been made with Coleman as Chris Wilder wants to add more experience to his squad for the 2026/27 season.
The Blades are only expected to offer Coleman a one-year contract, on a reduced salary to his previous Everton deal, with Wilder expected to speak to the experienced right-back before a return to full preseason training this month.