Sources have told ESPN that several top European clubs have reached out to Ansu's agent, Jorge Mendes, but the Spain international has made it clear he wants to remain at Barca. ESPN has confirmed that Barcelona chief Mateu Alemany met Mendes in Porto on Monday to discuss the player's future.
Sources added that the player's new deal will include a staggered salary which increases each season as Barca continue to fight the financial effects of the pandemic.
"I know they are close to agreeing a new contract with Ansu," Barca coach Koeman said in a news conference on Tuesday. "It's big news for Barca because we're talking about someone that can mark the club's long-term future."
Ansu, 18, returned from injury in September after 10 months on the sidelines with a goal off the bench against Levante.
He also marked his first start since last November with a goal in Sunday's 3-1 win over Valencia.
His contract -- which expires in 2022 and was negotiated by his previous agent, Rodrigo Messi -- includes an option to extend by two years, but there is confusion over whether Barca would be able to execute it unilaterally.
Various agents consulted by ESPN said they would not be able to as minors can only sign three-year deals. Sources at Barca, meanwhile, would not confirm if the clause has any value or not, but have always stressed the aim is to reach a fresh agreement with Mendes.
Ansu, who has scored 15 goals in 47 appearances for Barca, will become the second youngster to sign a new deal this month if he puts pen to paper.
Pedri is one of three players injured, along with Martin Braithwaite and Ousmane Dembele, and will miss Wednesday's crunch Champions League game against Dynamo Kiev at Camp Nou, while Eric Garcia is suspended.
"Of course it is a decisive game for qualification," Koeman said. "We have to win to keep our chances alive of getting through the group.
"There is nothing for it but to win the match. We know exactly what we must do. Getting three points now is the only way to get through this phase of the competition."
Since winning the Champions League in 2015, Barca have gradually lost touch with Europe's best teams and Koeman said there are various reasons for that.
"It is because the big teams have improved a lot and Barca, in the last five years, have dropped a level," he said. "I don't know why exactly because I can only opine on the time I have been here, but there has been a change.
"There are teams these days that have balanced squads with 23 international players and depth on the bench. The financial situation is much better [at other clubs] than ours. It all has an influence."