Liam Delap
Image caption, Delap has scored 13 goals in 67 Premier League appearances
The 23-year-old is expected to undergo a medical and sign a long-term contract at the City Ground this week.
Delap's move comes a year after he joined Chelsea from Ipswich Town for £30m amid competition from Manchester United and Everton.
However, Chelsea made him available for sale this summer after he scored just one Premier League goal in a previous campaign disrupted by shoulder and hamstring injuries.
Forest have already signed defender Ousmane Diomande from Sporting for £34m, alongside free agents, Austrian midfielder Xaver Schlager and goalkeeper Steve Benda.
They sold England midfielder Elliot Anderson to Manchester City for a club-record £116m and striker Taiwo Awoniyi to Coventry City for £9m.
Delap's arrival would provide competition for strikers Chris Wood and Igor Jesus.
Chelsea have also signed two strikers this summer in Emmanuel Emegha from Strasbourg and Danny Welbeck from Brighton.
More to follow.