The seamer claimed his 500th Test wicket as he helped his side secure a win over the West Indies.
The captain wants Joe Root to take his players to the Caribbean.
Broad hounded the tourists out for 197 in the morning and returned to take two more wickets in their second innings.
Bowler is three wickets shy of 500.
The tourists were all out for 197 at Old Trafford.
Jason Holder gives little away about selection for Old Trafford but likes what he sees from the off-spinner.
The West Indies have not beaten major opposition overseas in a Test series of three or more matches since 1992/93.
Jermaine Blackwood hit a match-winning 95 for the Windies at Southampton.
Holder claimed career-best figures of six for 42 to put Ben Stokes’ side under pressure.
The hosts had resumed on 35 for one after a rain-ruined start to the series.