Yorkshire have expressed "disappointment" after the England & Wales Cricket Board (ECB) refused their request to field Jonny Bairstow in this week's Country Championship decider.
While a club statement says the wicketkeeper-batsman "wanted to play", captain Andrew Gale confirmed spinner Adil Rashid has asked to be rested.
Yorkshire face leaders Middlesex in their final match, starting on Tuesday.
Bairstow and Rashid are in England's squad to tour Bangladesh in October.
An ECB spokesperson said: "We understand Yorkshire's disappointment but stress that Jonny Bairstow's absence has been known for some time.
"Director of England cricket Andrew Strauss talks regularly with all counties about England international players and it was made clear in July that Bairstow would not be available for the last two games of the season.
"As was explained, it was felt important that he has a period to rest and recover ahead of the winter tours to Bangladesh and India - which will see England cricketers face three ODIs and seven Test matches in the space of two-and-a-half months."
Yorkshire, second in the Division One table and nine points adrift of Middlesex, are looking to win a third successive Championship title.
When asked on social media if Rashid had asked to rest, Gale tweeted: "Yes, he wants to rest. That's his decision. I'll take 11 lads on the field who will give everything to win".
Yorkshire have questioned why Bairstow remains unavailable, having last played in England's one-day international defeat by Pakistan on 4 September.
"Members, supporters and other stakeholders in the game will wonder why this permission has been refused," the statement added.
Yorkshire say the request from director of cricket Martyn Moxon to have Bairstow - a player who is not centrally contracted with the ECB - available was turned down by Strauss and England coach Trevor Bayliss.
The club also pointed out that other England players selected to tour Bangladesh have featured in county cricket in recent weeks.
Test captain Alastair Cook played for Essex against Leicestershire and Worcestershire in Division Two, although he is not part of the England one-day set-up - while other Bangladesh-bound players including Jos Buttler, Ben Stokes, Steven Finn, Mark Wood, Liam Dawson and Jason Roy have featured in the County Championship.
Three Yorkshire players who are in the England squads for Bangladesh - David Willey, Liam Plunkett and Gary Ballance - are available to face Middlesex this week.
"Moxon works closely with England due to the fact that six players from Yorkshire have represented their country regularly over the last 12 months," Yorkshire's statement added.
"Bayliss' approach has been to see how the player feels, and this was respected when Bairstow said that he needed a rest after the one-day series.
"Bairstow has played five days of cricket in five weeks since the Oval Test match [against Pakistan], which finished on Sunday 14 August."