The 21-year-old has been excellent since making himself a mainstay of the Killie first-team in 2016.
This led to Bundesliga 2 side Nurnberg making two bids for his transfer earlier this summer, both of which were rejected by Kilmarnock.
It is also said that Celtic are looking at the Scottish international as a possible replacement for Kieran Tierney.
For the meantime, Taylor remains a Kilmarnock player and he is focused on nothing but continuing to prove his worth to manager Angelo Alessio.
He said: “I’m contracted to Kilmarnock so I’ve just got to keep doing what I can. If that’s enough to impress other teams then that can only be a positive. I’ve not had to speak to the manager about it yet because there’s not been a bid come in for me.
“There were two offers from Nurnberg earlier in the window, but both were rejected so it was out of my hands. I just got on with training at Kilmarnock.
“If and when a bid was to come in that was accepted then it would be discussed.
“With social media you are seeing the odd bits and bobs about it, but you don’t really have any choice, you have got to do your job on a Saturday.
“If you are not doing that the suitors and talk about moves will quickly go away. So it’s important to get the head down and just work hard.”