There is also interest in him from his former club Southampton and Turkish side Fenerbahce.
Speaking at a press conference today, Omur was asked about his links with Liverpool and said playing in Europe is his aim.
”Liverpool is a very important club," Omur said.
“Of course, these offers are something that our club can talk about first. I want to achieve some success here. Without success here I do not have to go to Europe.
“My priority is Trabzonspor but I have a dream to play in Europe, I hope I play there one day. My dream is to succeed here and then go to Europe."
Liverpool transfer news: Abdulkadir Omur has spoken out about a move to Liverpool (Image: GETTY)
Liverpool still favourites for league title say Burley and Mariner
So far this transfer window, Liverpool have allowed Dominic Solanke and Nathaniel Clyne to leave the club and join Bournemouth.
And Klopp says he is unlikely to replace them.
"Probably not," said Klopp when asked if replacements for Solanke and Clyne would be signed.
"Football is a business but we also need to care about people.
"For Dom it was absolutely right for him to go. He was unlucky that when there was space for him, he had injuries.
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
Liverpool transfer news: Abdulkadir Omur is valued at around £27million (Image: GETTY)
"He trained pretty well but it's difficult to maintain confidence when you're not playing particularly at that age. Bournemouth made a good offer, to be honest. We want to sign young players and keep them, but we don't want to block them.
"Having an option like Clyney is good. When I first came in he played almost every game, was always fit and important.
"Then he got his back problem and it took quite a while. Then there was change in the team, Joe [Gomez] was fit and Trent [Alexander-Arnold] came up.
"Clyney asked if he could go, I thought about it, then said yes you can as we have other options and younger boys coming up.
"You can always keep a player but to keep him in right shape with right amount of confidence that's not always easy."