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After putting seven past Spartak Moscow, the goals have dried up for Jurgen Klopp's side.
A disappointing 1-1 draw in the Merseyside derby was followed up with a 0-0 stalemate against West Brom in midweek.
And Molby is concerned that despite the manager's rotation policy, some of his recruits are not performing to the best of their abilities.
"Maybe one or two of the players are a little heavy-legged," Molby said in his Liverpool Echo column.
"We do rely heavily on our energy and our pace so if you take a little bit off that you can look a little bit ordinary.
"Tempo is not always about how quick you move, it’s about how quick you move the ball and see things.
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“We do rely heavily on our energy and our pace so if you take a little bit off that you can look a little bit ordinary”
Jan Molby
"That’s been a problem the last two games. We haven’t been quick or decisive enough, not getting the ball into key areas quick enough.
"It’s about being sharper in your brain, seeing things quicker."
Liverpool travel south to take on Eddie Howe's youthful cherries side on Sunday (4.30pm).
They lost the corresponding fixture last season. A enthralling match which finished 4-3 to the Cherries.
Danish midfielder Molby made 283 appearances for Liverpool, twice winning the League and FA Cup.
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And he's believes the south coast outfit will once again be able to compete at the same level as the Reds.
"I always worry when we play Bournemouth and it’s because of their energy," he continued.
"Liverpool’s strength is energy and pace and I certainly think they can almost match us.
"That’s what happened last year where they just kept going.
"I think it will be a difficult game on Sunday and they played very well at Old Trafford on Wednesday."