The American, 29, beat Greece’s Christina Linardatou, 35, on points by unanimous decision in Detroit.
She avenged her only defeat, against Linardatou via split decision in 2018.
“Katie Taylor I want you; Chantelle Cameron, Amanda Serrano,” Baumgardner said when asked what was next.
Baumgardner took her record to 15 wins from 16 fights after scoring heavily in the opening rounds before hanging on for victory against Linardatou.
She then hinted in her post-fight interview she would be willing to step up a weight division – from super-featherweight at 9st 4lb (59kg) to lightweight at 9st 9lb (61.4kg) – to take on Ireland’s Taylor.
The Ohio-born boxer holds all the titles – WBA, WBC, IBF, WBO and The Ring – at super-featherweight, while Taylor, 37, holds all the belts at lightweight.
Taylor, however, is set for an autumn rematch with England’s Cameron, 32, in Dublin after losing their light-welterweight contest in May.
Baumgardner also mentioned Cameron, who holds all the belts at light welterweight (10st/63.6kg), and Puerto Rican Serrano, 34, the undisputed champion at featherweight (9st/57.3kg), as possible next opponents.
But she also said she had unfinished business in her natural weight division.
“I will continue to defend my titles at 130 [9st 4lbs/59kg] because I can do that,” added Baumgardner.
“I’m great, I’m getting better. I can always work on something – I’m not perfect. One thing about me, I’m a student of the game. I will keep learning and keep on applying.”
Elsewhere, Sunderland’s Josh Kelly, 29, maintained his unbeaten run at light-middleweight with the 15th win of his career, against Argentina’s Gabriel Alberto Corzo, 28, in Newcastle.
Written by: Debby Eselebor