Anderson, who recently became the highest Test wicket taker among pacers with 600 scalps during the home series against Pakistan, and Kohli have had some intriguing battles over the years.
Anderson, 38, made history when he had Pakistan captain Azhar Ali caught at slip by England skipper Joe Root in the drawn third Test at Southampton on Tuesday.
The Ashes series is scheduled to be played between November 2021 and January 2022 in Australia.
Anderson, who is currently the fourth-highest wicket-taker in the longest format of the game, asserted that 700 wickets feat might be within his reach.
Anderson has moved back to the top-10 after briefly dropping out of it since the preceding home series against the West Indies.
ICC rankings: Virat Kohli, Rohit Sharma maintain top spots among ODI batsmen, Jasprit Bumrah uncontested
India's wicketkeeper-batsman KL Rahul is in second place in the T20 rankings for batsmen behind Pakistan's Babar Azam and ahead of Australian white-ball skipper Aaron Finch.
Anderson became only the fourth bowler in Test cricket history to reach the mark with Anil Kumble (619), Shane Warne (708) and Muttiah Muralitharan (800) being the others.
Anderson becomes the first fast bowler to reach the landmark when he had Pakistan's Azhar Ali caught by Joe Root on the final day of the third Test at Southampton.
Anderson made his England debut in Melbourne in December 2002, taking a modest 1-46 in six overs but he improved on the tour and won himself a place in England's squad for the 2003 World Cup.
The only bowlers with more Test wickets than the 38-year-old Anderson are a trio of retired spinners.
The 38-year-old ended the fourth day of the final Test between England and Pakistan a wicket short of the elusive 600-wicket mark.
Anderson started Day 4 needing two wickets to become the first fast bowler to reach 600 in Tests, and managed to take one — that of Abid Ali (42) — during a lengthy third session at the Rose Bowl.
Anderson's exploits saw Pakistan being dismissed for 273 as England enforced a follow-on with the visitors still 310 runs behind.
Anderson took his tally to 592 when he sent back Pakistan opener Shan Masood and skipper Azhar Ali on the opening day of the second Test.
The left-hander's exit saw Anderson move to within nine wickets of becoming the first paceman to take 600 in Tests.