The midfielder's first campaign with the Reds was curtailed by a troublesome shoulder problem but Champions League winner Hamann is confident that Allen offers reason for optimism.
"It's a big step up when you go from Swansea to Liverpool but he had a fantastic start," Hamann told liverpoolfc.com.
"He was absolutely outstanding for the first few months then he missed a couple of games, Lucas has come back in the team - who missed the early parts of the season through injury - and then he found it hard to get back into the team.
"But I think for the first year he's done ever so well and you've got to give him time, he's only young. He showed his potential, if anything he'll only get better and I think there's a lot to look forward to.
"If he adds skills to his game then I think he can play in various positions in the centre of midfield because he's a clever player, he's a very good passer of the ball, he spots danger and he's a team player."