Anderson went past McGrath's tally of 563 Test wickets on Tuesday, 11 September when he dismissed India's Mohammed Shami on the fifth day of the fifth and final Test at The Oval. Shami's was the last wicket to fall as England won the game by 118 runs and pocketed the five-match series 4-1.
Only three spinners – Anil Kumble (619), Shane Warne (708) and Muttiah Muralitharan (800) – are now ahead of the English swing king in the overall list.
McGrath has backed Anderson to breach the 600-wicket mark, which is only 36 wickets away. "Just to see Jimmy now, he looks fit and keen and running around, it depends on what he wants to do. He has gone past me and I think the next bar is 600 Test wickets," McGrath told BBC.
"If he can get to 600 Test wickets, that's an incredible effort, and if he is still got that drive, that passion to get yourself up, to put the hard work in off the field to carry you through on the field... if he has still got that desire, then he can play as long as he wants."
Congratulations to @jimmy9 on passing @glennmcgrath11 to move to fourth in the all-time top wicket takers in Test list, with the most wickets by a pace bowler! 👏 #ENGvIND pic.twitter.com/P7iY3M4z3E
— ICC (@ICC) September 11, 2018
McGrath finished his career with 563 wickets from 124 Tests, the last of which he played against England in 2007, and coincidentally, his last Test wicket was none other than Anderson. Anderson is 36 now, but McGrath believes that the Englishman has more to offer, and Kumble's tally should be the next target for him.
"I think he's still got little bit left in the tank yet," McGrath said. "I'd like to see Jimmy go and get 600 and then whether he wants to try and knock off one of these dodgy spinners that are still at the top of the tree. I think Kumble is about 619. That's within range."