The Scottish international has been heavily linked with a transfer away from the Stadium of Light in recent weeks, with Celtic rumoured to be showing a serious interest.
However, Spurs are ready to beat the Glasgow giants to the 26-year-old as they plot forward thinking additions.
Prior to Sherwood’s arrival the London club had one of the Premier League’s more ineffectual attacks, but there have been signs of improvement since then.
However, their new boss is still keen to bolster his options, and sees Fletcher as an ideal candidate to challenge Emmanuel Adebayor and Roberto Soldado for a starting berth.
The former Wolves man has a proven track record in the English top tier, which appeals to Sherwood who is desperate to keep his side in the hunt for Champions League qualification.
Sunderland value their man – who earns in the region of £50,000-per-week – at around £10m, which has put Tottenham ahead of the likes of Celtic and Hull in the battle for his services.