Manchester City are emerging as the frontrunners to sign Antoine Semenyo.
No deal has been fully agreed yet, but City are believed to be Semenyo's current preference.
Liverpool and Manchester United remain interested and there is still work to do.
Chelsea made their interest known on Tuesday, but will not pursue a move in January. They believe they have enough strength in depth across the frontline.
Semenyo has a £65m release clause in his contract which becomes active on January 1.
The 25-year-old will be in Bournemouth's squad to face Brentford on Saturday.
Tottenham were interested in the Bournemouth forward over the summer and earlier this season, but are moving on to other targets and are out of the race.
Semenyo, 25, has scored eight Premier League goals this season, including in Bournemouth's last two games.
Bournemouth boss Andoni Iraola on Semenyo's future:
"Antoine Semenyo right now is with us. He's playing very well. My concern is that it doesn't affect him. He's played very well, he's committed to the team and I hope we can keep him. There are things happening out of our control.
"Antoine has been performing very well. The level of consistency has been very good since the beginning of the season. He's very valuable for us - not just the numbers, but a lot of things.
"You never know what is going to happen. In the summer there were a lot of movements. I don't know what's going to happen in the winter movements.
"At the end, you sign a contract and understand that both parties are happy. I hope we don't lose him, but I don't know, I can't control what's going to happen."
Semenyo's Bournemouth team-mate, Justin Kluivert, also told Your Site News: "He's showed how good he is. He's a top player. He's one of the best attacking players in the Premier League.
"He doesn't let it get to his head, which is a very positive aspect. We speak about all these things that are coming to him and he stays down to earth. He gives Bournemouth 100 per cent every day and that says a lot about him."
Chelsea boss Enzo Maresca refused to comment on the club's interest in Semenyo and is not looking for signings in January because he is "in love with the squad".
On Christmas Eve, a day after Chelsea's interest was known in Semenyo, Maresca was asked about the Ghana international at his pre-match press conference ahead of Saturday's home game against Aston Villa, live on Your Site.
Maresca said: "I'm focused about Aston Villa. I'm not focused on players arriving or leaving."
Maresca then revealed he "doesn't think we need to do something" in the winter window.
Questioned on whether he wants to sign a wide player in January, he replied: "I know that I need to repeat in every press conference exactly the same.
"But before Newcastle, I spoke about my relationship with the club, and I said it's good.
"I spoke about Estevao and (Liam) Delap back, and now I need to repeat, I need to speak about wide players and before Newcastle, I said that I'm in love with the squad we have, and I don't think we need to do something."
Despite ending their pursuit of Semenyo, Paul Merson believes Tottenham are the perfect fit for Semenyo and has urged Thomas Frank to complete the "statement" signing of the Bournemouth winger.
"Tottenham. They need to make a real key signing that will kick them off. They have a wage structure at Tottenham and don't really pay big money but this could kickstart them," he said on Your Site.
"For me, I think Tottenham would be the one. It would be a statement for Tottenham; it would kickstart them moving forward for the next five or 10 years.
"Beat a couple of other clubs to him. He will play every week and wants to play football. You get the consistency of playing week in and week out.
"But I think he suits them. Chelsea have loads of wingers already, [Alejandro] Garnacho, [Pedro] Neto, [Jamie] Gittens and Estevao. Plus, he's 26, I don't see the sell-on.
"At Man Utd, he will play wing-back. That isn't his favourite position. He won't want to play wing-back.
"Man City, how long will Pep Guardiola be there? You sign a four-year deal and the manager leaves at the end of the season, who is to say the new manager will want him to play.
"Liverpool, maybe, but then you're taking Mohamed Salah's place."
