Manchester United forward Rashford, 26, has struggled for form this season, scoring seven goals and managing two assists in 33 league appearances.
He played in seven England games this season before being left out against Belgium in March.
Rashford shared a screenshot of the training squad on social media, with a message “wishing Gareth and the boys all the best” for the tournament.
Henderson joined Al-Ettifaq in Saudi Arabia from Liverpool last summer but left them to join a struggling Ajax side in January.
Southgate continued to pick him following his move to the Saudi Pro League, though he was booed by some England fans on his first game back in the country, against Australia at Wembley in October, which the England manager said at the time “defies logic”.
Henderson was in the squad for March friendlies against Brazil and Belgium but did not play.
Southgate will have to cut at least seven players when he confirms his final squad of up to 26 players for the tournament in Germany, with a deadline of midnight on 7 June.
Full England Squad
Goalkeepers: Dean Henderson (Crystal Palace), Jordan Pickford (Everton), Aaron Ramsdale (Arsenal), James Trafford (Burnley).
Defenders: Jarrad Branthwaite (Everton), Lewis Dunk (Brighton), Joe Gomez (Liverpool), Marc Guehi (Crystal Palace), Ezri Konsa (Aston Villa), Harry Maguire (Manchester United), Jarell Quansah (Liverpool), Luke Shaw (Manchester United), John Stones (Manchester City), Kieran Trippier (Newcastle), Kyle Walker (Manchester City)
Midfielders: Trent Alexander-Arnold (Liverpool), Conor Gallagher (Chelsea), Curtis Jones (Liverpool), Kobbie Mainoo (Manchester United), Declan Rice (Arsenal), Adam Wharton (Crystal Palace).
Forwards: Jude Bellingham (Real Madrid), Jarrod Bowen (West Ham), Eberechi Eze (Crystal Palace), Phil Foden (Manchester City), Jack Grealish (Manchester City), Anthony Gordon (Newcastle), Harry Kane (Bayern Munich), James Maddison (Tottenham), Cole Palmer (Chelsea), Bukayo Saka (Arsenal), Ivan Toney (Brentford), Ollie Watkins (Aston Villa).
Marcus Rashford and Jordan Henderson are the big names to be left out of Gareth Southgate’s provisional 33-man England squad for Euro 2024.
