Bess has returned to parent club Somerset after his one-month loan ended.
Yorkshire tried to extend it but Somerset want him back to boost their hopes of winning the County Championship.
Yorkshire first team coach Andrew Gale said: “He’s certainly someone we’d love to sign full-time. We’ll try everything we can to do that. We haven’t made an offer because he’s still got 18 months left at Somerset.
“Unless he turns round to Somerset and says that he wants to leave, then we can’t make him an offer, but Somerset would have to agree.”
Gale believes that Bess could grow increasingly frustrated if he continues to play second fiddle to Somerset’s first-choice spinner Jack Leach.
It was a lack of opportunity at Taunton that prompted Bess’s loan switch to Yorkshire in the first place.
The 21-year-old off-spinner took seven wickets in four Championship appearances for the White Rose, bowling well in largely unhelpful conditions, and also chipped in with 156 runs – including 91 not out against Essex at Emerald Headingley.
Bess’s final appearance came yesterday against Surrey at Guildford, where a rain-ruined game finished as a draw.
“First and foremost, Dom wants to play cricket,” said Gale.
“Next week, when we’re at York, Somerset haven’t got a game, but we could only extend his loan by two weeks at a time, and they want him available for Chelmsford the week after.
“If he doesn’t play there, they’re going to have a frustrated player on their hands, but, at the same time, Leach might get picked in the Ashes coming up, meaning Dom is suddenly Somerset’s first-choice spinner, so things can change fast.”
What is beyond doubt is how highly Yorkshire regard Bess – both as a cricketer and character.
Gale paid him a nice tribute when he recently described the Exeter-born player as someone who “looks like a Yorkshire cricketer”.
“He’s a great character and someone we’d love to have around more,” he added.
“He’s very mature and street-smart in a cricketing sense. Whether we’ll see him again this season, or in the future, I’m not sure. But he’s certainly been a great fit for us.”
Bess’s last act in a Yorkshire shirt – for the time being at least – was paradoxically unsuccessful as he perished for a golden duck at Woodbridge Road.
He was one of six wickets to fall during a dramatic morning in which Yorkshire collapsed from an overnight 58-1 to 93-7 in reply to Surrey’s first innings 313.
After rain accounted for 32 overs from 11.40am, having already claimed the first day and much of the third, Yorkshire were dismissed for 148 on the stroke of tea on day four, failing by 16 runs to save the follow-on. Openers Adam Lyth and Will Fraine ensured there were no alarms in the 13.3 overs possible thereafter, guiding their side to 30-0.
“With the bat in the morning, I thought we probably took the position that we were in for granted,” said Gale.
“We weren’t quite switched on, and if you’re not switched on against good sides like Surrey they can do some damage to you, and that’s what they did.
“There was a tricky little period there but we got a draw out of the game and it hasn’t burst the bubble. It’s been a frustrating few days and we weren’t at our best, but we’re still playing some good cricket and have got some good confidence in the camp.”
A final day that had promised nothing more than a bland battle for bonus points developed into something more interesting as Yorkshire wickets fell with unseemly regularity. The tone was set from the first ball, Gary Ballance fending Morne Morkel to Dean Elgar in the gully.
In overcast conditions, Morkel followed up with two more wickets in his next over, Fraine and Jack Leaning both caught behind, the latter quite brilliantly as Ben Foakes dived full length to his right to take the ball one-handed in front of first slip.
Jonny Tattersall slashed Jordan Clark high to Rikki Clarke at first slip, the same combination accounting for Bess next ball.
Jordan Thompson kept out the hat-trick delivery as Clark missed out on repeating a feat he performed against Yorkshire last summer in the colours of Lancashire, when he memorably dismissed Joe Root, Kane Williamson and Jonny Bairstow at Old Trafford in what was described as the greatest hat-trick ever in terms of the quality of victims.
Following a brief rain delay, Clarke had Tom Kohler-Cadmore caught down the leg-side and, after a longer stoppage, Yorkshire captain Steve Patterson caught behind too. Morkel bowled Ben Coad and then ended the innings with a fine catch on the long-leg boundary as Matt Dunn removed Thompson for the highest score of 34.
Trailing by 165 when they followed-on with 38 overs left in the game, Yorkshire had reached 24-0 when bad light stole a further four overs. They returned for another five overs before yet more bad light saw the sides shake hands on a day when 56.3 overs were lost in total.