Liverpool: Coutinho may regret leaving club says pundit
Defender Lovren, 29, has been heavily linked with a switch to AC Milan but Sky Sports say an approach is yet to be made and that they have no plans to sell.
Lovren was firmly behind Virgil van Dijk and Joel Matip in the Liverpool pecking order last season and made only 11 Premier League starts.
He failed to make a single appearances in the Champions League despite being at the forefront of the celebrations after the Reds beat Tottenham in the final.
With Joe Gomez fit again, he could be further out of favour when the 2019-20 campaign gets underway but Klopp is reportedly keen to keep him.
Selling the Croatian would leave Liverpool needing to replace him and Klopp has already said he does not expect to be busy in the summer transfer window.
After Croatia beat Spain 3-2 in the UEFA Nations League win November 2018, Lovren taunted Sergio Ramos on Instagram after he appeared to elbow the Real Madrid star during the game.
He was later found guilty of breaching UEFA rules for anyone “whose conduct is insulting or otherwise violates the basic rules of decent conduct.”
Meanwhile, Liverpool hero John Aldridge has urged his former club to sell if the right offer comes in.
Lovren made no appearances in last season's Champions League (Image: GETTY)
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Lovren is behind Joel Matip and Virgil van Dijk in the Liverpool pecking order (Image: GETTY)
"It would not be a surprise to me to see Dejan Lovren leaving Liverpool this summer," he told the Irish Independent.
"He has certainly improved under the guidance of Jurgen Klopp and his coaching staff, while the presence of Virgil van Dijk alongside him has made a huge difference to a player who famously said he was one of the best defenders in the world after his performances at the World Cup last summer.
"I don't think he is anywhere near as good as he thinks he is and Klopp clearly agrees, as he favoured Joel Matip ahead of Lovren for most of last season and young Joe Gomez is also waiting in the wings as a potential partner for Van Dijk.
"Lovren will be on big money at Liverpool and if the club are looking to free up some space on the wage bill, he may be a player urged to leave as I don't see him getting too much first team football when Matip and Gomez are fit."