Rashford scored 30 goals and helped Manchester United return to the Champions League in 2022-23 but has not been able to recapture that form.
Southgate has named a 33-strong training squad that has to be cut to a maximum of 26 players by June 7.
The Manchester United forward and Ajax midfielder missed out, despite Southgate naming an expanded 33-man Three Lions squad for Euro 2024
The iconic Germany star returned to the national team earlier this year