Lamps wants the England Under-20 defender on a permanent deal for £500,000, says The Sun.
And he hopes the offer of regular first-team football can help secure his services.
Mitchell, 21, was on loan at Hearts in Scotland last season.
And after impressing north of the border he is weighing up his next move for the upcoming season.
Heading back to the Scottish Premiership is an option for the left-back.