The Swansea City manager was speaking out after Taylor asked to speak to Newcastle United when they tabled a bid that meant he could ask for permission to talk.
Rodgers told the Evening Post "What I will say is that there will be no player at this club who does not want to be here
"If a player does decide that they want to speak to another club, they can go, simple as that.
"I only want players who want to play for Swansea City.
"We are in one of the greatest eras in this club's history.
"We are going through a wonderful journey which started last season and we are going into the most competitive league in the world, so we need to have people with a competitive mindset and the right mentality.
"I will give my life for the club and the other players woll – we are only a team when everyone wants to be in that team.
"I need to speak to Neil, I can only say at this moment that I am bitterly disappointed that a young player who came out of non league and made 30 odd appearances last season would want to talk to another club at this point in his career.
"He is at a club with people who will help develop his career. I understand that players only have short careers and they have to do the best for themselves and their families.
"But I think it's poor how this has been dealt with. I need to get the reaction of the player and see where he is coming from, but I am disappointed that one or two issues that have come up here have come up."