That’s according to The Argus after the Seagulls were linked with the 25-year-old Colombian forward overnight.
It was claimed a “formal offer” would arrive from Graham Potter’s side and that River coach Marcelo Gallardo had advised him to move to Europe if possible.
However, it appears there is no interest from Albion in Borre as his contract ticks down into the final few months.
Meanwhile, Bournemouth boss Jonathan Woodgate believes Arnaut Danjuma can go right to the very top.
The Dutchman was linked with Albion and Southampton last week following his impressive season in the Championship.
And Woodgate, in charge of the Cherries until the end of the season, is tipping the 24-year-old for big things.
"He can go as high as he wants to, but he’s got to always want more, always try to be that best," he told the Daily Echo.
“If something doesn’t go right in a game, be disappointed, try and improve constantly and that’s what he’s doing.
“I’m really pleased and I’ve been very impressed. I had high expectations about Arnie, really high expectations.”
Here are the latest transfer headlines surrounding Brighton and their Premier League rivals:
![Paris Saint-Germain are working on a deal to bring Manchester City striker Sergio Aguero to the French capital after it was announced the 32-year-old will leave the Citizen at the end of the season. (Todo Fichajes - in Spanish)](https://www.thestar.co.uk/webimg/b25lY21zOjNlOTVjZjU0LTdjMTAtNGQ2MC1hNzRhLTk4MThkZTBiOTkyYTo2M2U1NDU1ZC1kMTFkLTRlNDItYjlhYy1kNmI4YzVlMTE1MzI=.jpg?crop=3:2&width=800)
1. PSG working on Aguero deal
Paris Saint-Germain are working on a deal to bring Manchester City striker Sergio Aguero to the French capital after it was announced the 32-year-old will leave the Citizen at the end of the season. (Todo Fichajes - in Spanish) Photo: Gareth Copley
![Everton will consider offers for Yerry Mina in order to raise funds to sign Napoli defender Kalidou Koulibaly. The Merseyside club believe the Colombian will fetch in just under £20million. (Football Insider)](https://www.thestar.co.uk/webimg/b25lY21zOjM5ZTA2MjE4LTMzY2MtNDJkNy05ZmE2LWRkNmQyMDNmZWUzMDphZjQ5YmQyMS0wNTIzLTRmMjctYmJkNS0zMTlkYzdlMTE5ZmI=.jpg?crop=3:2&width=800)
2. Everton open to selling Mina
Everton will consider offers for Yerry Mina in order to raise funds to sign Napoli defender Kalidou Koulibaly. The Merseyside club believe the Colombian will fetch in just under £20million. (Football Insider) Photo: Clive Brunskill
![Arsenal are the latest club to show interest in signing Fiorentina forward Dusan Vlahovic, joining the likes of Tottenham, AC Milan, RB Leipzig, Roma and Atletico Madrid in pursuit of the Serbian. (Calcio Mercato)](https://www.thestar.co.uk/webimg/b25lY21zOjMxZTQ2Zjg3LThkNzktNDI5MC1iNDNjLWE4MmNjZDFkMWJhZTo1ZjQxM2E5NS0wYmU4LTQwODktYmQyZC1lOWRjNGUxNjQ2YTY=.jpg?crop=3:2&width=800)
3. Arsenal join Vlahovic chase
Arsenal are the latest club to show interest in signing Fiorentina forward Dusan Vlahovic, joining the likes of Tottenham, AC Milan, RB Leipzig, Roma and Atletico Madrid in pursuit of the Serbian. (Calcio Mercato) Photo: Francesco Pecoraro
![Manchester United have joined Tottenham and Liverpool in the race for RB Leipzig captain Marcel Sabitzer, who has made it clear to the Bundesliga club that he wants to leave this summer. (Bild via The Sun)](https://www.thestar.co.uk/webimg/b25lY21zOjYzYTczMmI5LWZjNDAtNDIxNS1hMTE3LWNmZTEzNTU5ODNmNjo4NzJlY2U0ZS03MTUxLTRmZjEtYjQ5My03ZmE0NTAzMTBlNzQ=.jpg?crop=3:2&width=800)
4. Man Utd join Sabitzer race
Manchester United have joined Tottenham and Liverpool in the race for RB Leipzig captain Marcel Sabitzer, who has made it clear to the Bundesliga club that he wants to leave this summer. (Bild via The Sun) Photo: ANNEGRET HILSE