Steve Cotterill wanted him permanently after a successful long term loan there last season, but Glenn - who handed the Northern Ireland under-21 player his Premiership debut on the last day of the season at Middlesbrough - reckons he has what it takes to perform at the very top.
"Grant has been offered a new contract and tells me he wants to remain a West Ham player," says Glenn.
"He certainly enjoyed his time at Cheltenham and we could see a great difference in him when he came back and played a couple of reserve games, and because he did so well in those he crept onto the bench against Middlesbrough.
"And, although he only got five minutes, he at least got on to the pitch and had a very small taste of Premiership football.
"We could see that he had grown up and toughened up a lot, looked more mature and more a man than the boy he was when he left us.
"Whenever a new manager is appointed the slate is wiped clean, everyone comes in on an equal footing and it is up to all the individual players to impress the new manager and force their way into the team."