Kevan, 41, has made it clear he does not want the job on a permanent basis.
Cotterill is the fourth different boss at Meadow Lane this season, following Ian McParland, Kevan and Hans Backe.
Kevan, who worked with Cotterill at Stoke and Burnley, will revert to his former role as assistant manager.
Minister for Veterans Kevan Jones will be meeting the Normandy Veterans Association's leaders next week to discuss the issue.
Kevan Fraser, 17, managed to get inside Lybster Primary in Caithness through an insecure door on 21 October last year.
"I don't want to be manager but it's a case of carrying on as we are, " Kevan told BBC Radio Nottingham.
The defence minister, Kevan Jones, confirmed PM's story in the House of Commons on Thursday following a question from a Conservative MP.
Kevan Craft, from Runcorn, Cheshire, suffered from whiplash after a driver who was on her mobile phone crashed into his car at 60mph.
Charles Walker and Kevan Jones supported the bill, both have been widely praised for speaking out about their own struggles with mental illness .
The former Burnley boss, 45, takes over just a week after the Magpies named Dave Kevan as caretaker boss until the end of the current campaign.
But shadow defence minister Kevan Jones opened an opposition-led debate on defence reform on 26 June 2012, telling MPs that this figure was a "completely erroneous myth".
Trew had said on Tuesday that he was eager to retain Kevan, who was first-team coach at Meadow Lane, until at least the end of the season.
Minutes later Kevan George cleared a header by Olave off the goal line following a corner kick and a collision that left two Columbus players on the pitch.
Shadow defence minister Kevan Jones said it was "absolutely right and necessary" for the UK to retain an independent nuclear deterrent but the cost needed to be taken into account.
Labour MP Kevan Jones agreed with the shadow local government minister, claiming that the government was "expecting councils and local people to walk blindly into the future" and that the bill was "being rushed through with undue haste".
Federico Higuain converted the penalty kick and for the next 16 minutes it seemed like the game winner, especially after Columbus goaltender Andy Gruenebaum stopped a hard shot by Juninho from the top of the box in the 83rd minute and defender Kevan George cleared a header by Olave off the goal line minutes later.
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