Both men were last night fighting for their lives after they were discovered near a bus stop in Ossett, near Wakefield.
Officers were called to Manor Road at 7.20am yesterday.
The men, who have not been named, were taken to Pinderfields Hospital, where they were both described as being in a "critical condition" in the intensive care unit.
Officers from West Yorkshire Police's Homicide and Major Enquiry Team are leading the investigation,
A spokesman for West Yorkshire Police said last night: "Officers are currently working to confirm the identities of the two men, who are both described as white and between their thirties and forties."
He added that inquiries so far have led officers to believe that the men may have spent Saturday evening in Leeds.
It is not clear how long the men had been at the bus stop or who found them there.
Last night police would not elaborate on the nature of the men's injuries.
They are, however, appealing for anyone who witnessed any suspicious activity in Manor Road and in Ossett between Saturday evening and 7.20am yesterday to contact them.
Officers also want to hear from anyone who can help to identify the two men.
Witnesses or anyone who has information which can help to identify the men are urged to contact West Yorkshire Police on 0845 6060606.