The Wales left-back has been a regular fixture in Garry Monk's side this season following the departure of Ben Davies to Tottenham.
Taylor's current deal expires at the end of next term and Jenkins told the South Wales Evening Post: "That needs to be looked at between now and the summer; it's an obvious one for us to sort out."
Jenkins added: "With Neil, this is the first time for a long time that he has had a good run of games [after injury disrupted his 2012-13 season], and it always takes players time to get up to speed.
"As the season has gone on and Neil has played more games, I think we have seen that he is getting back to his best.
"That is great for Neil and great for us as a club."
"I talk to his agent regularly. There are ongoing discussions and we'll see where they take us."
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