The 23-year-old, who still has three years left on his contract, endured a difficult time at Spurs last season and was used as a bit-part player by both Andre Villas-Boas and Tim Sherwood.
Holtby made just six league starts and five more in cup competitions before being shipped out on loan in January to Fulham, who were relegated to the Championship.
A number of Premier League clubs were keen on signing the playmaker during the previous transfer window and have recently renewed their interest.
But Holtby's representative, Marcus Noack, told Sky Sports: “Lewis is optimistic about the future at Spurs.
“There is a new manager there now which means it's a fresh start for him and a fresh start for everyone.
“He is happy at Tottenham and has a good feeling there. He wants to stay and prove himself and be part of the team.”
New Spurs boss Pochettino has already allowed midfielder Jake Livermore to join Hull City, where he spent the last year on loan, but there is not expected to be a significant turnover of players at the club this summer.
Tottenham remain locked in talks with Swansea City over left-back Ben Davies, who is valued at £12million by the Welsh club, and are hopeful that a deal can be agreed.
Holtby, who has three caps for Germany, signed for Spurs from Schalke in January 2013 but missed out on his country's 2014 World Cup squad.