Glenn McGrath, who ended his career for Australia in 2007, is at the top of the pile with 563 wickets. But he expects to be dethroned in a few days when the fourth Test between India and England begins at Southampton.
"I have an awful lot of respect for Jimmy," he told the Daily Mail. "Good luck to him. I believe once he goes past me he will never be beaten.
"Records are nice and I've been very proud to have taken more wickets than any fast bowler in Test history, but any high is there to be beaten and I will be equally proud of Jimmy when he goes past me because the fast bowlers' union has to stick together, whichever country we come from."
"I noted how he swung the ball both ways conventionally, because it's a real art form. Not many have been able to do that. I can only really think of Wasim Akram, who is another great of the game"
There is a reason McGrath is certain no modern fast bowler can catch up with Anderson. "Once Jimmy goes past me it will be interesting to see where he wants to set the bar. With the nature of the game these days, and the amount of Twenty20 cricket, I believe no fast bowler will ever go past him.
"Being a fast bowler is the toughest job in the game and people do not see the hard work off the field that goes into spending as much time at the top as Jimmy has. We put ourselves through a lot more pain than anyone else.
"So for Anderson to still be at the top of his game after 15 years in international cricket and with so many overs under his belt just shows his work ethic and his physical and mental strength."
McGrath had an inkling that Anderson would be breaking records. "I've always said Jimmy was class, ever since I played against him in what became my last Test series in 2006-07. I noted how he swung the ball both ways conventionally, because it's a real art form. Not many have been able to do that. I can only really think of Wasim Akram, who is another great of the game, who could do that as skilfully."
McGrath, however, was doubtful of that. "I'm not sure how keen he will be on that but there's no reason why he can't go on for some time yet if he still has that passion and drive.
"He looks in fantastic shape, running around like a young fella, and hasn't put on any weight. He is clearly as hungry and strong as ever. The fact that Trevor would even suggest reaching 40 and still playing is a big compliment.
"I always wondered if I would know the right time to retire. After that first Ashes Test in Brisbane in 2006 I had no intention of stopping. I was still focused and wanted a thousand international wickets. I was still driven.
"Then I went home after that match, went to bed, woke up and it just wasn't important to me any more. It hit me just like that and I retired from Test cricket at the end of that series after 124 games. I knew it was time to hang the boots up.
"Maybe that will happen with Jimmy but there's not much sign of it yet. And with the way he's going it will be up to him to decide how long he goes on for. I can't imagine any selector being daft enough to call time on him."
A long-standing criticism against England's highest wicket-taker is that he struggles in conditions that aren't suited to fast bowling. Three hundred and sixty one of his 557 wickets have come at home. So have 21 of his 26 five-wicket hauls.
"When the ball is swinging he's as good as anyone out there, but when it isn't he comes back towards the pack a little bit," McGrath said. "That was certainly the case early in his career but he's developed his skills as he's gone on and become much more effective overseas. When Jimmy plays at home with the Dukes ball he's second to none, but he has had to learn how to operate overseas with the Kookaburra ball that, to me, is not nearly as good to bowl with. It took him a while but he's done that now.
"So can Anderson get somewhere close to the three great spinners above me in the all-time wickets table? I reckon that once he's knocked my tally off the next goal will be 600 wickets and that would be an incredible feat.
"Then you have Anil Kumble on 619 which is feasible but I'm not sure how close Jimmy can get to Shane Warne on 708 or Muttiah Muralitharan on 800. Even someone as great as Anderson will find that a bit of a struggle."