GE Healthcare and private equity firms Carlyle Group Inc (CG.O) and Clayton, Dubilier & Rice (CD&R), which have been pursuing rival offers separately, are also through to the second round, the sources added.
Carlyle is bidding through its newly formed healthcare investment platform Atmas Health, according to one of the sources.
Medtronic has been taking offers for its patient monitoring and respiratory interventions businesses even as it presses on with preparations to spin them off to its shareholders.
ICU Medical, GE Healthcare, Carlyle and CD&R declined to comment.
The patient monitoring technology portfolio includes Nellcor pulse oximetry and BIS brain monitoring, while the respiratory interventions business comprises ventilators and breathing systems.