At 36, Anderson is at the twilight of his career but McGrath believes the Englishman is not yet done and the next target for him will definitely be Kumble's (619) record.
James Anderson became the most successful fast-bowler in Test history by claiming the final wicket to clinch England's 118-run victory.
A mediocre England team with a fragile batting line-up won the series by a comprehensive 4-1 margin after India were bowled out for 345 in pursuit of a mammoth target of 464.
Courtesy the twin hundreds by the former and current skipper, England declared their second innings on 423/8 with a massive target of 464 for the Indians.
His innings contained 11 fours and a mighty straight six of the bowling of English pace spearhead James Anderson.
The incident happened in the 29th over of India's innings when Anderson snatched his cap and jumper from umpire Kumar Dharmasena.
Stuart Broad and Sam Curran removed India's openers, then James Anderson and Ben Stokes tore through the middle order with two wickets each.
Broad can move into fourth place on this list at The Oval itself if he takes three more wickets during the match.
With Indian pacers doing a star turn with 38 out of the 46 wickets in three Tests being taken by them, the Bengal speedster said that it is their duty to deliver in conducive conditions.
The 36-year-old Anderson needs seven wickets to overtake McGrath's haul of 563 when he spearheads England's attack in the fourth Test against India.
For Indian team, the Trent Bridge Test will be their last chance to save the series after being outplayed in the first two Test matches.
Bayliss said Woakes looks primed to be a natural replacement for James Anderson when the time comes for the 36-year-old to hang up his boots.
The India captain played knocks of 23 and 17 even as his side succumbed to 107 and 130 for an innings and 159-run loss at the Lord's.
The home skipper hailed his team's bowling performance, which handed them a 2-0 lead in the five-match series.
England beat India at Lord's in the second Test by an innings and 159 runs to take a 2-0 lead in the five-match series.
India suffered an embarrassing 159-run innings defeat in the second Test against England after yet another batting failure on day four at Lord's.
Anderson is only the second bowler, after legendary Sri Lankan spinner, Muttiah Muralitharan, to have claimed 100 Test wickets at a single venue.
Anderson picked up five wickets and was at his lethal best from his very first ball when he bowled Indian opener Murali Vijay with intimidating swing that left the batsman numb in the first innings of Lord's Test.
India were not helped by the fact that Cheteshwar Pujara was run out for the third time this year after a horrendous mix up with skipper Virat Kohli.
Anderson took his 27th Test five-wicket haul, picking 5/20, as India were bowled out for 107 runs with rain intervening thrice during this innings.
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