But you can also say, 'I can smell something burn(ed)(t). (the past participle/adjective form) It's no longer burning but you can still smell the burn(ed)(t) smell.
"burn" is also possible but least likely to be used. 'I can smell something burn.' indicates my ability to smell that particular smell. Maybe my sense of smell is very bad and I almost can't smell anything, but I can smell something burn. But for this unlikely use, you can also use "burn(ed)(t)" or "burning".