Saints skipper Lallana has been in superb form this season, earning his first England call-up, and Cork believes he should be an automatic pick for this summer's tournament in Brazil.
Boss Mauricio Pochettino believes Lallana could play for Spain or Brazil, and Cork agrees, having been left open-mouthed when he first saw the attacking midfielder during a loan spell on the south coast in 2008.
"He was running past people in training and I was saying 'it is crazy how good he is'," Cork, who made his move to Saints permanent in 2011, said.
"I think Adam has got unbelievable qualities and is such a good player. I see it every day in training.
"Some of the stuff I see you have to take a second look at and take a step back and say 'what just happened?' because he is so good.
"The qualities he has are just amazing. He can create something out of nothing all the time. It is just good knowing that you can sit back and someone like that, Jay Rodriguez or Rickie Lambert is going to do something magical and win you a game.
"There is no reason why Adam couldn't fit into any of the top sides in Europe or world football because he is that good."
Asked if Lallana should be an automatic choice for Roy Hodgson's England squad this summer, Cork said: "Yeah, I think so. I think he offers something different to what other English players have.
"We have a lot of wingers that are quite direct and quite pacy and I think Adam is a bit more clever. He can see the ball, manipulate his feet quicker than some other players.
"I think just having that cleverness in the England team is just something different we could maybe work with."
Cork has been in fine form himself this season, with Lallana saying he made the difference when he came off the bench at half-time in the 3-0 victory over Fulham.
Saints rejected a deadline day bid from Swansea for Cork and he is happy he is staying at St Mary's.
"I think if you had asked me earlier in the season, I might have said something different," he said.
"Obviously Victor Wanyama came in and I wasn't playing as many games as I would like to have been playing at the start of the season.
"That changed in November, December time, playing a lot more games and I think it showed that I still had a part to play in the squad and in the team.
"Hopefully if I can keep the form going, I can still have a big part to play in the team. I will see what happens in the future and towards the end of the season."