Wales international Allen was in superb form for the Swans in their debut Premier League campaign last season as they secured an 11th-placed finish.
The performances of the 22-year-old have caught the attention of a number of England’s top sides.
And Bellamy has urged Rodgers to bring his compatriot to Anfield over the summer with the Reds set to go through a rebuilding process.
"He [Allen] is special. He has made so many key passes for Swansea last season and I would be shocked if Liverpool did not go for him this summer," he said.
"He’s a Brendan Rodgers player, he fits Liverpool to a tee.
"If Liverpool are able to secure him, they will have a real gem of a player."
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