A run of four consecutive defeats saw Tindall get the sack this week with the Cherries sixth in the Championship table, nine points off the automatic promotion spots.
According to the Daily Mail (opens in new tab), the club has already received a lot of interest in the vacancy, including from Premier League greats Vieira and Terry.
Terry is an assistant coach at Aston Villa (opens in new tab) but harbours ambitions of moving into a top job, and the compensation required to take him away from Birmingham would not be an issue.
Vieira is looking for a new challenge after being sacked by Ligue 1 outfit Nice in December.
The former Gunners midfielder led New York City FC in MLS before his stint in France and has been linked with several Premier League jobs in recent years.
Eddie Howe’s return is considered unlikely, while Frank Lampard is expected to take some time out of the game following his sacking by Chelsea.
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