Cory Dixon, 30, and Ashley Holder, 33, are being sought after in connection with the double stabbing that took place in Medleys on Bristol Road South on March 9.
Officers were called to reports of disorder at about 2.20am and two men were taken to hospital with stab wounds.
A third man was also taken to hospital with a serious head injury. All three have since been discharged.
DC Darren Lennox, from force CID, said: “This was a shocking incident in which three people were seriously injured.
"Anyone with information on the whereabouts of Dixon and Holder are urged not to approach them but to get in touch immediately.
"Anyone harbouring these suspects is committing an offence and also could be jailed.”
If you have any information about the incident contact police via Live Chat at west-midlands.police.uk between 8am and midnight, call 101 anytime or contact Crimestoppers anonymously on 0800 555 111 quoting crime number 20BW/58079M/19.