Northern Ireland international O'Connor spent the end of the season at Lincoln and vowed never to play for Thordarson again while Elding also had a successful time with the Imps before finishing the campaign at Gresty Road.
But the Icelander has offered an olive branch to the pair following Crewe's relegation to League Two and told his club's official website. "Michael is ready to improve and he has a future here if he wants it. If he does there is a place in the team he can battle for. If he doesn't respond he won't be a part of it.
"It's the same with Ant. He played the last two games for us and did a reasonable job.
"He is committed and hard-working and I was impressed. He might be interested in heading back to Lincoln or that part of the world, but as far as I'm concerned he will be my player."
Meanwhile, the agent of Dennis Lawrence, who spent the second half of the season on loan at Crewe from Swansea, has told the Sentinel that Crewe have "first refusal" on the defender this summer.