Measures proposed for that date would see theatres and concert halls welcoming back audiences, and conferences and exhibitions resuming, the PA news agency understands.
The limit on gatherings in indoor domestic settings could also potentially increase from six to 10.
A 15-person cap on the size of outdoor domestic gatherings would remain but a five-household limit would be removed.
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Household bubbling provisions in the rules would also be dropped.
If ministers agree to all or some of the proposals at Thursday afternoon’s virtual meeting of the powersharing administration, the July 26 date would be indicative and subject to ratification on July 22.
The meeting comes amid rising rates of coronavirus infection in the region.
The rapid spread of the Delta variant, first identified in India, and ongoing efforts to increase vaccine uptake will be key factors in the ministers’ deliberations.
Other proposals earmarked for the end of the month include allowing close contact services to accept walk-in customers without the need for pre-booked appointments.
Restrictions on indoor live music would be relaxed, including an end to a requirement for the sound to be kept to an ambient level.
The proposals would facilitate a full return of live music and dancing at events.
While most measures under consideration are categorised as lower risk “green” relaxations, ministers will also examine the potential for a number of “amber” steps on July 26 as well.
Those include the end of social distancing requirements for outdoor activities and a reduction of the distance to one metre for relevant indoor settings.
The proposals also include removing the legal requirement to wear face coverings in places of worship.
Another amber measure would see school bubbling and the use of face masks in classrooms removed from guidance ahead of the start of the autumn term.
A further proposal would relax some of the current restrictions on how MoT tests are carried out in Northern Ireland
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