Marc Kosicke says the German will consider his options in 2022.
"Jurgen's contract is still valid until 2022 and it is an open secret that the club would like to extend," Kosicke told Spox.
"We still have a little time for that. We must wait and see how everything develops and whether climate change will bring better weather to England or only to Germany.
"One should not underestimate it [bad weather annoying Klopp], anyway. I remember that in November or December, Liverpool first asked for a contract extension. I said: 'Let's wait'.
"Ulla [Klopp's wife] and Jurgen get up in the morning and it's dark. When they meet again in the evening, it is also dark or it is grey and there is drizzle.
"During the winter break in Germany, if the weather is really bad, the clubs go on vacation for two weeks, then come back and fly directly to the training camp in the sun for several days.
"During this time, the coaches in England sometimes have to prepare for up to 13 games. They are already exhausted and it's not so easy."