The former England all-rounder, who has played for the county for the past 17 years, is unhappy with a new deal offered by the club.
Director of cricket Martyn Moxon said: “Bres has had a contract offered. At the minute it’s unsigned, so we’re waiting to see what comes of that.
“I think he’s just looking at his options. We’ve offered him a deal, he’s not completely happy with that, so he’s exploring his options.”
Bresnan, 33, is no longer a guaranteed first-team regular.
He lost his place in the ongoing Royal London Cup competition, but returned to the side last week to help the club into the knockout stages with a victory against Northants.
Bresnan helped Yorkshire over the line with an unbeaten 13 – having earlier captured 2-40 from eight overs – to set up a quarter-final play-off against Essex at Chelmsford on Thursday.
He remains a potentially key figure for Yorkshire in all three formats.
“The contract offer was made way before the recent Royal London games, so it’s prior to that competition starting,” said Moxon.
“As I say, he’s not completely happy with the offer, so he’s exploring his options, simple as that.”