Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
The 26-year-old was already contracted until 2014 but Malky Mackay has moved to tie him down for the long-term after an impressive start to the season.
Taylor, who has established himself as the Bluebirds' first choice full-back, joined from Middlesbrough in July last year.
"Andrew is one of those players who sometimes goes under the radar when it comes to making headlines, but he is always one of the first names on the teamsheet for me," Mackay told the club's official website.
"He's been utterly consistent in his attitude, application and performance since he joined us almost eighteen months ago.
"He is one of the guys I know I can absolutely count on week in, week out, so I was really pleased that he is as happy with us as we are with him. Thanks to Andrew and his representatives for working with us to make it a relatively straight forward process."