The 83-year-old, who won the Tatton seat in 1997 on an anti-sleaze platform, is understood to have been approached by a senior Lib Dem figure to stand in Owen Paterson’s old seat in the December 16 by-election.
But according to a party source, former broadcaster Mr Bell rejected the offer, saying he was "too old" and that he didn’t believe any party could overturn the Tories near-23,000 majority.
Lib Dem leader Ed Davey, who visited Whitchurch on Sunday, is said to be keen on bringing in a ‘big hitter’ to contest the North Shropshire seat, which is vacant due to Mr Paterson standing down after he was found to have been paid for lobbying.
The party is understood to have approached Mr Bell at his home in London to sound him out about attempting to repeat his against the odds feat of 24 years ago.
Back then he trounced Tory Neil Hamilton, who was embroiled in sleaze allegations, overturning his majority of almost 22,000.
According to the Lib Dem source, Mr Bell was invited to move to Shropshire to temporarily take up residence in a home owned by a wealthy Lib Dem member.
The source told the Star: “Martin was considered the ideal candidate, but he said he was too old and that no party would be able to overturn the Tory majority.”
Mr Bell stood down in the Cheshire seat of Tatton after serving one term.
He stood against another Conservative MP in 2001, reducing Eric Pickles’ majority in Brentwood and Ongar by two thirds, and made an unsuccessful attempt to become an MEP in 2004.
Another Lib Dem source said the candidate selection process was ongoing, and that support for the party was "on the rise" across North Shropshire because people were "sick of being taken for granted" by the Conservative government.
Other potential names in the hat for the Lib Dems include former Ludlow MP Matthew Green and Shropshire councillor Alex Wagner.
Labour is looking at a number of local candidates, although the party is believed to consider the seat a long-shot and is more focused on targeting a number of Black Country constituencies in the next general election.
Kirsty Walmsley is standing for Reform UK, while Monaco-based consultant Russell Dean is standing for 'The Party Party' on an anti-sleaze platform.
North Shropshire Conservatives are set to choose their candidate at a meeting of the association on Saturday.