The deputy first minister was answering questions in the Assembly today, Monday, June 28.
Ms O’Neill told assembly members that proposals under consideration include the reopening of youth services and live music.
These both initially had to be delayed due to concerns about the Delta variant.
The planned resumption of live music on June 21 had been delayed and given an indicative date ofJuly 5.
It will need to be considered by ministers in line with health advice.
On Monday, the North of Ireland recorded 211 further cases of Covid-19 and no further deaths, while on Sunday it passed the 2 million mark for the total number of vaccines administered.
Derry City and Strabane District Council recorded a further 44 cases, a fall of 12.
Two people are currently being treated in intensive care units and two people are on ventilators.
Ms O’Neill said the Executive would “revisit” health advice on Thursday, July 1, as well as other measures including the reopening of theatres and indoor seated venues, residential stays for youth services, allowing walk-ins for close contact services and reopening conference centres and exhibition centres.
“Alongside all of that work officials are looking ahead to next week’s Executive and what potentially we can bring forward there also, all the while informed by scientific and medical advice,” said Ms O’Neill.
“All things being equal we’d hope to progress these things on Thursday provided that’s supported by health and science.”
In England, new Health Secretary Sajid Javid is expected to announce later today whether July 19 will declared ‘freedom day’ and an end to nearly all Covid-19 restrictions.