The former Chelsea man has quickly returned to his best form and helped Albion to a lofty ninth in the Premier League standings.
Lamptey joined Albion in January 2020 for just £3m from Chelsea as the England youth international went in search of regular first team football.
His path at Chelsea was blocked by the excellent Reece James and his brave decision to leave Stamford Bridge proved the right one as his career has flourished under the guidance of Albion head coach Graham Potter.
Arsenal remain keen on the flying wing back, while Man United continue to monitor the situation as they seek more attacking options down their right flank.
But Tottenham have also entered the race and are looking to freshen up their squad and kick-start the Antonio Conte era.
Brighton however are under no pressure to sell but an offer similar to the £50m they received when Ben White joined Arsenal last year could tempt the Seagulls to part with a player who has played just 31 Premier League matches - scoring once with five assists.
Potter, never one too keen to address transfer talk during the window, responded to the Lamptey reports at his press conference ahead of their FA Cup third round match at West Brom this Saturday.
"I would expect all our players to be with us," said Potter when asked if Lamptey would still be an Albion player come the end of the window.
"A lot of speculation out there but nothing to report. The fact there is speculation out there means you are doing something quite well.
"As a team and as a club we are okay with that. It is what it is.
"We are not a selling club and we don't have to sell anybody at all but you never know so you have to aware of that.
Asked if any bids have been received so far, Potter simply replied: "Nope!"
In term of potential arrivals the Albion head coach added: "I'm happy with the squad we have and I think we can still get better as a group.
"We have not reached the maximum in terms of how we are performing.
"I'm excited to see that develop. You never know what the window brings in terms of what comes in from the outside but we are open to that."