Allaway aiming for Premiership job
The 19-year-old signed a three-month loan deal with Paul Groves's side as cover for Danny Coyne, while regular number two Steve Croudson recovers from injury.
The England Under-19 international is tipped as having a bright future in the game despite his young age and lack of first team action.
With Paul Robinson and Nigel Martyn ahead in the goalkeeper pecking order at Leeds, the former Reading custodian has been told by Terry Venables to use his time with Grimsby as a learning process.
Allaway revealed that he is determined to make himself into a Premiership keeper in the future.
He told the Grimsby Telegraph: "My aim is to be a top Premiership keeper.
"They don't normally develop until their late 20s, so time is easily on my side.
"The manager (Venables) said to me that I haven't got much League experience and that coming here would be good for my development.
"Hopefully when I go back I'll be able to show them what I can do.
"I wasn't going to get in the team at Leeds so it's good that this came up."
Allaway is confident that he can perform for The Mariners` first team, should Coyne be unavailable and hopes his abilities will be of Division One standard.
He added: "I'm here at Grimsby to develop and I'll be playing in the reserves.
"I want to do what I can to help the club and give my best while I'm here.
"I'd like to think I'm ready for the First Division if it happens.
"I've played in the reserves at Leeds against teams like Manchester United so if I'm thrown in I hope I'm capable of playing well."