The Blades have seen Chris Wilder leave the club following their fall to the bottom of the Premier League table.
They only have 14 points from their 30 games and are almost guaranteed to fall into the Championship.
Did Chris Wilder hold Sheffield United together?
Tindall is currently on the books at the Blades, assisting Paul Heckingbottom as a coach as the club look to retain their dignity before the end of the season.
He has only been in charge of one club, managing Bournemouth for six months after the departure of Eddie Howe.
They won just one of their Tindall’s final eight league games but Yorkshire Live reports that he is on the shortlist to replace Wilder permanently.
Gillespie is surprised by that, and has insisted that the Blades need to take their time, as it’ll be difficult to convince a manager to come into the club for the remainder of such a difficult season.
He told TIF: “He obviously didn’t last too long at Bournemouth. I’d be surprised at that one, that’s not to say it won’t happen, I suppose they’re not in a hurry. You want to get these appointments right.
“Would you want to be coming in as a manager for the remaining games when you’re effectively [down]. I know it’s mathematically possible to stay up but that isn’t going to happen, we’re wise enough to know that.”