Keita has already been subject of a £57million offer from Liverpool, which was rejected by last season's surprise Bundesliga runners up.
However, the Guinea international has made his intentions clear he wants to leave and join the Reds this summer.
His stance has seemingly not gone down well with people at Leipzig, who are now keen to get shot of him.
Solhekol says Liverpool are expected to make another improved offer for the 22-year-old in the coming days.
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Kaveh Solhekol says RB Leipzig now want to sell Liverpool target Naby Keita
A Liverpool bid of more than £60million for Naby Keita should be on its way this week
Kaveh Solhekol on Liverpool target Naby Keita
"We are expecting some progress on Naby Keita to Liverpool," Solhekol said on Sky Sports News.
"Liverpool flew to Hong Kong yesterday but no let up in their efforts to try and sign Naby Keita.
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"We are expecting them to make a second bid for the RB Leipzig midfielder.
Naby Keita wants to move to Liverpool this summer
"Keita has told Leipzig he wants to leave, he's told them he wants to move to Liverpool.
"A £57million offer has been rejected but senior figures at Leipzig now want to sell Keita.
"A Liverpool bid of more than £60million should be on its way this week."