James Anderson would love to return to the England Test team.
Anderson and Broad were left out of the West Indies tour.
Without the duo, England lost the Test series in the Caribbean.
Anderson said that he and Stuart were hoping that their careers wouldn't end.
Anderson and Broad have both taken a record number of Tests for England.
The appointment of Rob Key as managing director has reopened the door for the 39-year-old fast bowler, with both saying they want Anderson and Broad to return.
Anderson said that it still means that we have to put in some performances with our counties to prove that we are playing well enough to make the final XI.
Because of the situation and not having people in these roles, you are unsure of what will happen. It's nice to have clarity now.
Anderson said that the natural leader who has the respect of the group and a clear idea of how he wants the team to play was the obvious choice for captain.
He said he would love to be a part of that. English cricket needs to win more test matches.
England will face New Zealand and South Africa in a Test series this summer, as well as play the final Test of last summer's five-game series against India, which was postponed due to Covid-19 concerns.