Fry told BBC Radio Cambridgeshire: "Gary Johnson has got him down as a major target and we've given him until next week to make his mind up.
"The talks have gone very well and we hope to hear that he will join us."
Hibbert started his career with Port Vale, before moving to Preston in 2005.
There are better 'big-striker' options out there but given Posh's tight budget next year he could be the best cheap and cheerful option
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After failing to start a league game for Preston, he joined Shrewsbury in 2007 and scored 30 goals in 111 games.
"We're hopeful he will sign, but his wife is having a baby and Shrewsbury have made him a very good offer," Fry said.
"But he got on well with Gary and I'm confident that if it's a football decision he will join us at Posh."
Hibbert has struggled with injury problems in the past, but was a virtual ever-present in the Shrews side last season.
Fry has said he can add power and strength to Johnson's squad and should compliment the club's current forwards.
"It gives Gary another option as we don't really have a physical presence up front and we need competition for places," he said.
Source: BBC Sport
Source: BBC Sport