The 27-year-old left-hander asked Mark Burstein, Gil Vernon and Dan Brent to award him $5.6 million, and the Braves argued during Thursday's session that he should be paid $5.1 million.
A decision is likely Friday.
Minor was 6-12 with a 4.77 ERA in 25 starts last year, when he missed the first month of the season because of shoulder soreness. He made $3.85 million.
He went 13-9 with a 3.21 ERA in 2013.