Assombalonga, 23, had three years remaining on the deal he signed on joining from Peterborough in 2014.
Forest owner Fawaz Al-Hasawi said he had turned down an offer from Premier League side Norwich for the forward.
Assombalonga, who missed much of the 2015-16 season with a serious knee injury, has scored 19 goals in 39 games for Championship side Forest.
His three goals this season have helped the club to seventh place after five games.
Meanwhile, Al Hasawi has said that the £13m received from the sale of Oliver Burke to German club RB Leipzig will be reinvested into the club.
"The money remains in the club, we could spend it in January or on a facility within the club," Al Hasawi told BBC Radio Nottingham.
"We are willing to reinvest it but I cannot go and get three or four players for the club. That is the manager's decision.
"We have to let him choose the right players for himself and respect that."
Winger Burke, 19, had netted four times in seven appearances this season and, despite his future potential, no sell-on clause was included in the Scot's transfer deal.
Al-Hasawi continued: "There is no sell-on clause for Burke as at first they offered £8m and I turned them down, then they offered £10m and I said 'no'.
"When they said £13m and we will pay it in one go without a sell-on clause, I said 'OK'.
"The money we got from the sale is good for the club, especially as they paid the money in one go. It's good business."

Colombia's Attorney General Eduardo Montealegre said the office was run by a criminal organisation that had intercepted emails from a Farc rebel negotiator and the government.
He said President Juan Manuel Santos was also "probably" targeted.
Peace talks began in Cuba in 2012 to try to end five decades of conflict.
"This office intercepted emails from the press chief of the Farc in (the Cuban capital) Havana, an institutional email from the national government, and two emails from Cuban journalists who are covering the peace process in Havana," Mr Montealegre told a news conference in Bogota.
"The purpose of this office, the purpose of the people who were involved in this criminal enterprise, was to sabotage, interfere and affect the peace process in Havana," he said.
"It appears that, through this office of interceptions, the emails of the president of the republic were also probably intercepted."
One person, Andres Sepulveda, was arrested for allegedly running the operation and selling the information he obtained to third parties.
The attorney general said they were investigating who was paying to gain access to the information.
The Farc, Colombia's largest guerrilla group, has been in talks with the government in Cuba since November 2012 to try to end the longest-running internal conflict in Latin America.
Hundreds of thousands of people have been killed and some three million more have been internally displaced since the two sides began fighting in the 1960s.
President Santos has said he hopes to sign a peace treaty with left-wing rebels this year.
Nottingham Forest striker Britt Assombalonga has signed a new five-year contract.
[NEXT_CONCEPT]
Colombian authorities say they have raided an office that illegally spied on rebel and government communication to try to undermine peace talks.