There are worries over the futures of the two Leeds youngsters, whose contracts both expire in 2017.
Taylor and Cook are yet to commit their futures to the Yorkshire club, and Evans has suggested that they are yet to be offered new terms.
Leeds fell into a similar situation with Sam Byram last January, when they were forced to sell the defender to West Ham United, as they did not want to risk losing him on a free.
There are still hopes that Cook and Taylor will sign new contracts with Leeds in the near future, but Evans could not confirm that either of the youngsters would certainly remain with the Whites.
"I can’t speak for those young men, but my conversations with them suggest that they want to be part of something special at Elland Road. They’ve told me that," he said.
"Part of my discussions towards the end of last season was before we think about new players let’s get Cook’s and Taylor’s futures sorted at Elland Road. They are equal to the best in the Championship. Hence why in January there was £20 million worth of offers for Premier League clubs for four different players."
Taylor and Cook have both expressed their happiness to be at Leeds, and their desire to guide the side to the Premier League previously.
However, their excellent performances at Championship level have attracted the attentions of top flight clubs.
Taylor has been linked with Sunderland, Liverpool and Crystal Palace, while Cook is reportedly interesting Manchester United and Arsenal, amongst others.
Leeds are likely to have to fend of interest in their prized prospects over the coming months, and their determination to keep hold of them could be tested.