Ottis Gibson, the Yorkshire head coach, said that Ballance was keen to play in the fixture against Hampshire.
The 32-year-old batsman has yet to represent the first XI this season as he continues to grapple with the fallout of the Azeem Rafiq racism affair.
The crisis saw the departures of more than 20 staff and officials and cost the club millions of pounds.
Ballance admitted using racial slurs against his former Yorkshire team-mate in their younger days in the context of two close friends exchanging insults on nights out. He said that he regretted his actions but has pointedly never apologised to Rafiq.
Yorkshire have stood by Ballance despite sacking 16 coaches and backroom staff for signing a letter which accused Rafiq of deliberately trying to bring down a club that released him in 2018.
Ballance has taken baby-steps in second team cricket in recent weeks, scoring two centuries in as many games, and although it is possible that he could play some part in Yorkshire’s 50-over campaign that starts on Tuesday when they host Northamptonshire at York Cricket Club, Gibson said that Yorkshire will leave it up to him.
“I’ve sort of left it to Gary with regards to how he’s feeling mentally,” said Gibson. “He’s played some second-team games and he’s been looking good.
“I spoke to him before the Hampshire game and he was keen to play in that game, but then he said to me he’s not sure because he’s still struggling obviously with what has happened.
“Some days he has good days and some days he doesn’t; he has bad days and so on. He didn’t feel like, I guess, being away from home for the four days or whatever; he didn’t feel comfortable with that. So we said, ‘Look, he’s not ready yet.’
“With what has happened to him, I listen to what he is saying to me. If he says, ‘I’m ready to go and I’m confident’, then I listen to that. If he’s saying,’ I’m not so sure’, then we also listen to that.”
As to the likelihood of Ballance playing in the 50-Over Cup, Gibson said: “There was a chance that he might have played at Scarborough, and there’s always that chance, I guess, but it depends on how he is mentally.
“It’s not a physical thing, or a batting thing, it’s just how he is mentally with what he’s been going through and what he’s been dealing with.”