James Anderson says it's 'nice to hear there's a chance' of returning to England set up
However, they were omitted from England's most recent tour to the West Indies - a series which they lost 1-0.
Leaving Anderson and Broad out was deemed as controversial though and at times, they were in desperate need of at least one of them in the team.
Ben Stokes has since been appointed Test captain, replacing Joe Root in the role and he wants the pair back in the squad.
"Stuart and I were hoping our careers weren't over. So it's nice to hear there's a chance," Anderson told the BBC.
"Because of the situation and not having people in these roles, you're just so unsure of what's going to happen. So now having that clarity is really nice."
On the chances of Anderson and Broad playing a part, Rob Key told Sky Sports News: "Yeah, they will.
"'I can't promise you you're going to play, all that type of stuff, you're just available for selection'. Then Ben Stokes was very clear on the fact he wants Jimmy and Broady to come back in.
Key added: "They just want to continue on this journey they've been on [with England]. They didn't want it to finish in the way that it possibly might have done. They were obviously both very happy to be up for selection for that first Test match."
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