The club want Rashid to help them in their quest to climb out of the County Championship relegation zone.
Yorkshire dropped into the bottom two after their seven-wicket defeat to Surrey at Scarborough, and first-team coach Andrew Gale has asked if the player would reverse his decision to play only white-ball cricket this summer.
“He said that he’d think about it, but I can’t see him making a U-turn,” said Gale. “It’s up to him. You never say never. If he finishes T20 and he feels like he wants to keep playing cricket then you never know.”
Rashid is unavailable as Yorkshire prepare to start their Vitality T20 Blast campaign against Durham at Emerald Headingley on Thursday due to his England commitments.
The 30-year-old is part of the squad for the three-match T20 series against India that starts on Tuesday and for the three-match one-day series against India that culminates at Headingley on July 17, which is England’s final white-ball game of the summer.
Rashid is then available for the bulk of Yorkshire’s T20 campaign, with the group stages finishing on August 17.
But the club still have seven Championship games left – exactly one half of their programme – as they aim to avoid sliding into Division Two.
Whether Rashid makes himself available for the Championship or not, the spin bowling situation is an area of concern.
Neither Karl Carver nor Azeem Rafiq have been able to command a regular Championship place with Yorkshire relying on the part-time spin of batsmen such as Adam Lyth and Jack Leaning.
Gale said that the club are actively looking to strengthen.
“The spin bowling area is something that we’re looking at,” he said.
“Whether we get someone this year, I’m not sure, but down the line, yeah. Maybe a loan or maybe a permanent signing. We’ll have to have a look at it.
“Rafa (Rafiq) is playing in the second team this week, so we’ll have a look at that with regards to the T20 coming up.”
Gale is confident that the club can pull clear of danger despite Yorkshire’s Championship predicament.
“I’m not getting too down,” he said. “I’m obviously gutted that we lost to Surrey, but I feel like the dressing room is still a good place.
“The team spirit is still there and there is still a togetherness there, and if we can keep that going we can turn the corner.”
Key to that aspiration is top-order batsmen scoring more runs, a perennial problem in recent times.
At the halfway stage Yorkshire’s leading run-scorer is 19-year-old Harry Brook (407), who also possesses the highest average (33.91) if you discount England’s Jonny Bairstow, who averages 45.25 from just two appearances.
Otherwise, of the top-order on duty at Scarborough, Gary Ballance averages 33.60, Jack Leaning 30.00, Adam Lyth 22.41, Cheteshwar Pujara 14.33 and Alex Lees 6.25.
“A few individuals just haven’t stood up, highly experienced players,” said Gale.
“We haven’t got a lot of options, and players need to start putting up their hands.”