The full-back, who will celebrate his 20th birthday next week, has agreed personal terms with the Reds and is poised to undergo a medical.
Gunter failed to make an impact at Tottenham following his £2million arrival from Cardiff in January 2008 making just 16 appearances for the Premier League club in all competitions.
He joined Forest on loan towards the end of last season and made eight appearances as Billy Davies' side steered clear of relegation from the Championship.
Gunter will become the Reds' fifth summer signing following David McGoldrick, Dele Adebola, Lee Camp and Paul Anderson to the east midlands club.
Meanwhile, Preston captain Paul McKenna is set for talks at the City Ground next week after the two clubs agreed a £750,000 fee for the 31-year-old midfielder.