Town boss Jimmy Quinn told the Shropshire Star: 'We've made him what we believe is a generous offer and he feels he is worth a bit more.'
The manager also indicated that the contract offer did include some coaching duties. O' Connor will miss tonight's Shropshire Senior Cup game against Bridgnorth.
This allows room for summer signing Ben Smith to make his debut in blue and amber.
The Shrews will look to build on their 3-2 victory over Northwich on Saturday. Town used a 3-5-2 formation and took a three-nil lead through Duane Darby (2) and Ian Fitzpatrick before conceding twice in the last ten minutes.
Assistant boss Dave Cooke told ShrewsWeb: 'It was a good work out for the lads and I thought we controlled the game until the last ten minutes.' He also praised the work of main striker Duane Darby.
*Town will not be signing former Bristol Rovers fullback Neil Arndale who played against Northwich.