The Shrewsbury chief responded with 'no comment' after reports in Humberside suggested the 27-year-old shot-stopper had handed in a transfer request at Blundell Park.
With tomorrow's 11pm deadline rapidly-approaching, it remains to be seen whether Hurst makes a move to bring his former goalkeeper to Greenhous Meadow.
Hurst and former joint-manager Rob Scott signed the goalkeeper just a few months into their Grimsby spell in 2011 and he went on to earn plaudits as the Mariners' No.1.
The Birmingham-born keeper, who spent time in Walsall's academy before moving on to Peterborough, has made 260 appearances for the Lincolnshire outfit.
He's played six times under new boss Marcus Bignot – who replaced Hurst following the boss's move to Shrewsbury – since December 17.
Bignot has instead favoured Dean Henderson, the on-loan Manchester United goalkeeper, who recently extended his loan for the rest of the campaign.
McKeown – a two-time Player of the Season at Grimsby – spoke to BBC Humber following the Mariners' 2-0 defeat at Stevenage, where he explained that a transfer request had been accepted.
"I want to play football, I feel like I've got no option," he said.
"It's not a decision I've taken likely. The manager's been very honest and told me I'm not going to play for the rest of the season."
McKeown refused to answer the question regarding Hurst's interest in bringing him to Shropshire.
Shrewsbury have four goalkeepers at the Meadow, Jayson Leutwiler, Mark Halstead, Callum Burton and Shaun Rowley.
Hurst has completed six signings so far this window, but revealed he is searching for a couple more additions before deadline.
But the boss remained coy on the specific positions he was targeting.