Anderson and Broad have over 1000 combined Test wickets, many of which have come in partnership.
But Vaughan says England need to manage their combination more effectively and be “realistic” about the chances of the pair reaching the next Ashes series in Australia in 2021-22.
“I don’t think it is right both of them play now,” Vaughan said on BBC Radio 5 Live.
“It might be that Broad plays one series and Anderson plays one series.
“They are not going to like it, but they are at that stage of their careers where England are going to have to manage the combination very smartly.”
England’s next Test action is a tour of New Zealand in November, for which an interim coach is likely to be appointed.
Anderson bowled just four overs in the Ashes series after aggravating a calf issue, but the 38-year-old is keen to resume his duties as the leader of the attack over the winter, and could be fit for that tour of New Zealand.
In his absence, Broad had a fine series, taking 23 wickets at an average of under 27, but the pair will be 39 and 35 by the time the next Ashes starts, and bowling fast on the hard and flatter pitches of Australia can be particularly wearing on ageing bodies.
Vaughan has also suggested England make a “big call” and leave out an established name for the New Zealand tour, perhaps reintroducing Surrey’s promising middle order batsman Ollie Pope to the side.
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It is likely that both Zak Crawley of Kent and Dominic Sibley of Warwickshire get opportunities at the top of the order during the course of the winter.
And with England having achieved the primary goal of outgoing coach Trevor Bayliss’ tenure by winning this summer’s World Cup, Vaughan is hoping there will be a shift in England’s red-ball attitude and fortunes – with regaining the Ashes in mind.
“I want to see a disciplined way of playing and the World Cup is in the bag now,” Vaughan said.
“The most important thing going forward is the Ashes in two years.
“It is the Test team that needs a real focus over two and a half years of real dedication and structure.
“It might be that some of the players who play all of the formats miss white-ball series to make sure that when the Tests are on they are absolutely fresh and ready to bat seven hours, because to win in Australia that is exactly what you require.
“You need a relentless nature with the ball and relentless discipline with the bat – and it has to come over a two-and-a-half-year window.”