The 41-year-old is the first seamer and only third bowler to have taken 700 Test wickets after spinners Shane Warne and Muttiah Muralitharan.
Anderson, however, has decided to end his Test career after England made it clear they wanted to move on ahead of the 2025/26 Ashes.
But England managing director Rob Key told reporters on Monday: "After the Lord's Test, Jimmy will continue in our set-up, and he'll help a bit more as a mentor."
Key added: "He has got so much to offer English cricket. We don't want to see that go.
"When we asked him, he was keen. He is going to have a lot of options. English cricket would be very lucky if he chooses to stay in the game."
Anderson is currently playing for Lancashire against Nottinghamshire in the County Championship at Southport, but his first-class future remains uncertain.
"What he does with Lancashire will probably work out after the Lord's Test," said Key.
England have included three uncapped players in their squad for the first two matches of a three-Test series against the West Indies, with Jamie Smith selected to keep wicket ahead of both Jonny Bairstow and Ben Foakes.
The 23-year-old Smith averages over 50 in the County Championship this season and celebrated his Test call-up by making exactly 100 for Surrey against Essex on Sunday.
He usually plays as a specialist batsman for Surrey with Foakes keeping wicket for the reigning county champions.
"Sometimes you're selecting people for what they're going to be as well, and where you think they can progress to," said Key.
"It's very much the start for Jamie Smith. We feel he's going to be a fantastic international cricketer."
Key, asked how Smith would cope with the demands of keeping wicket for 90 overs a day in a Test match when he is not a regular behind the stumps, said he had consulted several former England wicketkeepers in Chris Read, James Foster and Alec Stewart -- Smith's boss at Surrey.
"Some of the guys have been the best keepers in the country... We use them a lot really and we trust a lot of their opinions," Key explained.
'Wrong direction'
Key added Bairstow, 34, "needs to get back to what he was a couple of years ago", when the Yorkshireman hit six Test centuries in 2022.
Bairstow, however, has struggled lately after nearly a year out of the game following a horrifying leg break in a freak accident on a golf course.
"Generally his form, in all formats, has just been going slightly in the wrong direction," said 45-year-old former England batsman Key.
"It's an arduous task being a keeper and you want someone who can back up series after series. We weren't convinced that Jonny would be able to do that, especially at the stage of his career that he's at."
Key was speaking for the first time since defending champions England's defeat by India in the semi-finals of the T20 World Cup.
England won just one of their four matches against fellow Test sides during a tournament in the Caribbean and the United States following a woeful defence of their 50-over World Cup title in India last year.
Those reverses have called into question the positions of England white-ball captain Jos Buttler and coach Matthew Mott.
But Key said he would take his time regarding their future ahead of England's next white-ball series against Australia in September.
"I'm not going to rush anything on that," he said.
"At times I thought we showed how good we were and at times we were inconsistent. We'll let the dust settle on the World Cup and then move forward from there."
