The left-back started just 10 Premier League matches for the Welsh outfit in the last two seasons, with Ben Davies being the preferred option for manager Michael Laudrup and successor Garry Monk.
Taylor, 25, moved to the Liberty Stadium in 2010 when the international left Wrexham but his representative, Jamie Moralee, feels his client needs to have his situation clarified once and for all.
"Neil is a player that needs to play regularly, if that could happen at Swansea it would be ideal," Moralee told the South Wales Evening Post.
"Swansea is a fantastic club that has made a lot of progress and that's who Neil wants to play for. But if he can't be guaranteed regular football, I can't see him sitting on the bench for another season.
"That would be a third season in that position. That's no good for any player and Neil is at his peak. Hopefully he will be given that opportunity at Swansea, but if not Neil may have to pursue other avenues to get some games.
"Swansea are fortunate in that they have two international left-backs, but Neil hasn't played enough football of late.
"We need to talk about things sooner rather than later."