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Anderson missed the majority of the recent Ashes series against Australia because of a calf injury.
The 37-year-old bowler will still be sidelined for England's tour of New Zealand next month in Silverwood's first assignment since being promoted from bowling coach to succeed Trevor Bayliss.
But in a bid to prove his fitness for the following tour of South Africa, Anderson is training at Manchester City's Etihad Campus over the next two months alongside England's strength and conditioning team.
With 575 Test wickets to his name, a record for a seamer, Anderson is not about to be summarily discarded.
Former Essex coach Silverwood admitted Anderson and Stuart Broad are almost automatic selections provided they are both injury-free.
"If they're both fit, it's difficult to look past them, isn't it? It's a great headache to have. When you look at the amount of wickets they've got between them it's phenomenal," Silverwood said.
"Jimmy's great. He takes wickets, he's got a lot of knowledge in there that he can share with the players coming in.
"I think it will be up to him to let us know, and I think he will, when he's had enough, but who wouldn't want a world-class bowler like him in the line-up? He is phenomenal. He gets wickets all round the world.
"So yes I want him around as long as I can, but equally we've got to be realistic and say 'right we've got to do some future planning here'."
Silverwood seems content to defer to Morgan about when to quit, after the Dubliner presided over England's historic World Cup triumph this year.
The Irish batsman's future as limited-overs captain is uncertain beyond next year's T20 World Cup.
"The way he leads that one-day side and T20 side, and the influence he's got with the players, is phenomenal," Silverwood said.
"He's so respected and the ideas he has, moving them forward. My job is to give him as much support as I can, to help him get where he wants to get to with them.
"He's earned the right to tell us when he's had enough but certainly we've got to have one eye on transitioning that period."
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