The 24-year-old former Aston Villa man, capped at senior level by the USA, is a free agent this summer.
Former loanee Elliott Ward will be coming back to the City Ground next season as part of the Bournemouth side after signing a one-year deal with the newly-promoted Cherries.
Forest hero Stuart Pearce, meanwhile, is to leave his role as coach of the England Under-21 team at the end of his contract this month.
A poor showing in the European Championships recently spelled the end of Pearce's six-year stint.
***Update***Lichaj has sealed his move, telling BBC East Midlands Today: "Nottingham Forest were keen to sign me and I didn't hesitate at all to come here.
"My preferred position is right-back but I can play left-back as well.
"I always give 100% no matter what the situation is."