Van Dijk scored the winner for Liverpool against West Ham on Sunday as the Dutchman showed his importance to the side once again. Supporters were relieved to see Mohamed Salah pen a new deal last week and Carragher suggested that the announcements have to be separated as to not tone down the other.
"Listen, I think there may be some news on Virgil van Dijk next week," Carragher told Sky Sports. "I think the fact the Mo Salah news came out, maybe not trying to do two players on one day.
"Maybe not trying to steal the thunder of either of the players, Virgil van Dijk or Mo Salah. I think Mo Salah had his moment a few days ago and I'm sure that will be the case with Virgil van Dijk next week."
After the game Salah joked that Van Dijk has to decide his future and hopes he will be the next to sign an extension.
"I am glad that we managed to do that early, before the end of the season and hopefully Virgil will also be next. I'm just saying hopefully! Look he can do whatever he wants but I would love to see him here again next year."
Van Dijk remained coy and hinted that news of his contract extension will come very soon which will bring a sigh of relief for many fans who did not want to lose the iconic defender for free once the season ends.
"I can tell you I am very proud today to captain my 100th game for Liverpool. It was an emotional day because of the Hillsborough anniversary so that was the main focus to get three points and get a step closer to all of our dreams.
"Players, staff, everyone who is connected to Liverpool FC. That's the main thing because everyone knows how much I love this club and let's see what next week will look like."