The defender will have an operation on anterior cruciate ligament damage after the England international's reckless knee-high challenge in Saturday's derby.
A Merseyside Police spokesperson said: "We are now investigating a number of offensive Tweets made in relation to two Everton footballers".
Carragher believes that Liverpool are now short at the back as a result of Van Dijk's injury and should have "gone big" in the summer, but Klopp has taken umbrage with his comments and claimed he could not have kept another centre half happy.
'If anyone wants to tell us we made a mistake - I think Carragher mentioned already - there are a few reasons why they don't do this job'. We know it's a derby, and everyone wants to win the derby; sometimes you go over the top, but this was too much.
'It was not the only tackle like that. It was not only his tackle but also Richarlison's tackle on Thiago was also a nasty one. They are going to be more vulnerable defensively without Van Dijk because he's the best in the world - he's the best centre-half I've ever seen, he's that good.
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But Arizona has an issue similar to Dallas: both teams have a negative turnover margin heading into Monday night. In their last five-night games, the Cards have gone 0-4-1.so there's a bit of a hill to climb there.
"Dejan Lovren went and they didn't replace him so they only have three centre-backs and one of those, Joel Matip, is always injured", Carragher commented.
Midfielder Wijnaldum's attack was supported by manager Jurgen Klopp. "Both challenges were hard to accept, let me say it like this", Klopp said. Very often both players try to play the ball, but it was not the case in these two challenges, and it makes it hard to take.
"In the last four years we were leader of the fair play table and you don't get anything for that".
'We don't get anything for that, it's something people joke about. That means you can play football without these kinds of challenges. Fabinho, a central midfielder, is expected to partner Gomez in Amsterdam.