Guardiola signed a new two-year deal at Manchester City on Thursday, prompting more speculation the club may be able to convince Messi to move to the Etihad Stadium if he leaves Barcelona as a free agent in the summer.
Since taking the job in 2016, Guardiola has led the club to two Premier League titles, three EFL Cup triumphs and FA Cup glory on one occasion.
Guardiola and Klopp have become two of the best foreign managers to have worked in England, taking their respective clubs up a significant gear and playing superb football along the way.
Now midway through his fifth campaign in Manchester, the new contract extends what is already Guardiola's longest stay with any single club.
Guardiola's biggest successes have come domestically at City, where his side won the 2017-18 Premier League title with a record 100 points, and they retained their crown with a 98-point campaign the season after.
These Liverpool supporters on Twitter have been providing their thoughts on the "huge" news from their rivals, providing a mix of opinions.
City chairman Khaldoon Mubarak added: "It is testament to the qualities of the man that Pep Guardiola's passion and intelligent approach are now woven into the very fabric of the football we play and our culture as a club".
"The challenge for us is to continue improving and evolving, and I am very excited and about helping Manchester City do that".
Messi handed in a transfer request at the end of last season with City keeping an eye on the situation, but it was later withdrawn with Barca only allowing him to leave if his €700 million (£630m/$825m) release clause was met.
"I said when I signed the contract, we have many things to do". But he finishes this year the contract and I don't know what's going to happen in his mind.
City, who travel to Tottenham on Saturday, are now languishing in 10th place, six points behind leaders Leicester with a game in hand. It also goes to the stability and creativity at the heart of our football operations.
The Argentina forward ultimately chose to stay at Barcelona, somewhat against his own wishes, but his contract expires at the end of the season.