Alexander is now the favourite to take the helm for Town, a move which would delight the Mariners faithful.
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Keith helped Town win promotion to the old third division in his second season at the club. With Town keen to sign loan striker Neil Woods on a permanent deal, Alexander was offloaded to Stockport for £8,500 just weeks into the new campaign.
His time at Town brought 64 league starts and 19 goals. A gangly striker who was capable of moments of brilliance one minute yet unable to control the ball the next, Keith won the fans hearts with his determination and likeable character.
The 45-year-old started his managerial career at Lincoln back in 1993, he was dismissed after a poor season and set about establishing his coaching credentials at Mansfield.
A chance of management came at non-league Northwich Victoria. There Keith developed his management skills until he was appointed assistant at Lincoln to none other than Alan Buckley.
When Buckley was sacked by the clubs adminstrators, Alexander was appointed. By his own admission he was only appointed because he was the cheap option.
With no real budget to work with, Alexander set about raiding the non-league. With a brave battle against relegation expected, Lincoln exceeded all expectations and only a play-off final defeat to Bournemouth denied them promotion to Division Two.
This season Lincoln continued to impress although a more serious issue took centre stage. Alexander was taken ill and required major brain surgery. After a 3-month layoff, Keith returned to Sincil Bank full-time last week.
Whilst he is clearly happy at Lincoln and is keen to continue his work, the temptation of his first league club and personal ambition may prove too much should the offer come his way.
Alexander, who is out of contract in the summer, however kept coy over the issue, refusing to rule himself out of the running. He also added that he fancies Alan Buckley to get the job.
"I've got a job to do at Lincoln that I've started and, I think, is going pretty well," Alexander told the Grimsby Telegraph.
"I've been coming back to work on and off for the past month and things are going well here. We're not a million miles away.
"That's all I'm concentrating on at the moment. There's nothing more I can say.
"I haven't spoken to anyone at Grimsby but I've been in football long enough to know that things can change quickly.
"I like Grimsby as a club. Everyone knows that. I had a good time there and they deserve to be higher up in the league.
"Once you've been in the first division for a few years people think you should always be there, but that's not always the case.
"Alan Buckley is out of a job - he'll probably get it."