The Leeds United youngster has been linked with Burnley, West Bromwich Albion, Newcastle United and Middlesbrough in the summer transfer window.
Taylor, who is 22 years of age and can play as a left-back as well as a left-winger, is one of the most promising and most talented young players in the Championship.
The Englishman has been linked with moves away from Leeds this summer, with a number of clubs reported to be interested in securing his services.
According to The Guardian, Middlesbrough, who won promotion from the Championship to the Premier League at the end of last season, and West Bromwich Albion are interested in the English youngster, who is also claimed to be on the radar of Championship club Newcastle United.
The Sun has credited newly-promoted Premier League side Burnley with an interest in the former England Under-19 international defender.
Leeds manager Monk has claimed that Taylor will not be sold this summer.
“For sure, 100 per cent,” Monk told The Yorkshire Evening Post when asked if he expected Taylor to stay at Elland Road next season. “He has to be here.
“Charlie’s been great, he’s been fantastic in training and he’s very focused on what we’re doing. That’s not a problem.
“There’s no worries about it from my side and it’s business as usual. Charlie’s a big important part of what I’m doing.”
Taylor scored one goal and created 44 chances in 38 Championship appearances for Leeds during the 2015-16 season.
The 22-year-old had a pass accuracy of 74% and a shot accuracy of 36%, and won 61 headers, 40 dribbles and 59 tackles.