The previous licensee of the Jock's Lodge bar was removed and the pub temporarily closed last month by owners Scottish & Newcastle following the alleged attack on 24-year-old ex-boxer James Carlin on 7 March.
Mr Carlin was alleged to have been shot in the leg, stabbed in the upper leg and punched in the head.
S&N said today it hoped to reopen the pub at the beginning of June. A spokeswoman said: "Our aim is to reopen the pub as quickly as possible. We are in the final stages of finalising a new lessee. In the interim, we are taking the opportunity to redecorate the pub's interior. We are hoping to reopen in time for the World Cup starting on 11 June."
A city council spokeswoman said there would be no comment at this stage because it was still processing the application for the new lessee.
However, Labour councillor for Craigentinny and Duddingston, Ewan Aitken, hoped new management would improve the pub. He said: "Whilst I recognise the business imperative, I would want to be absolutely sure that S&N have taken enough time to make sure they have a high standard of management in the pub.
"There was a sense that there was lots of little things going on at the pub that shouldn't have been, whether it related to disputes, people being allowed to get completely drunk when they shouldn't have been, or too much noise from the beer garden. It had an aura of things happening that shouldn't have been, and I don't want to see that again."
Two men were arrested and charged over the incident at the pub, and both appeared at Edinburgh Sheriff Court last month.
Dean Scott, 27, appeared in court to face charges of assault with intent to murder and attempted murder. He was also accused of an offence under the Firearms Act 1968.
David Coutts, 20, appeared in court charged with assault with intent to murder.
Both men made no plea and were remanded in custody.