The club are hopeful of accomodating 2,892 spectators as they await the approval of proposals
T20 Blast fixtures 2021: Full schedule, dates
Glamorgan are free to welcome back their biggest crowds for 20 months after the lifting of restrictions by the Welsh government.
Outdoor sporting events and concerts in Wales are permitted to resume from Monday (June 7) for up to 10,000 people sitting or 4,000 standing.
One thousand fans were allowed to attend day one of the LV=Insurance County Championship match against Lancashire on Thursday (June 3), the first home game played in front of fans since the 2019 campaign, but only as part of a pilot scheme.
The other 17 first-class counties have been allowed fans since limits on crowds were adjusted in England from May 17.
In time for the start of their T20 Blast campaign which sees them face Gloucestershire and Essex in back-to-back home matches next week, first minister Mark Drakeford has announced supporters can be allowed back following a drop in Covid-19 infections and deaths.
Consultation with local authorities has seen Glamorgan submit a proposal for 2,892 to initially attend matches, based on the two-metre social-distancing regulation, with the club now awaiting approval.
Chief-executive Hugh Morris added: "Once again, we would like to thank our members, fans and partners for their patience and look forward to welcoming supporters back to Sophia Gardens in greater numbers."
The Cardiff venue is scheduled to host three internationals during the 2021 summer, with England set to face Sri Lanka in the first two T20s on June 23 and 24.
Eoin Morgan's side return to the Welsh capital on July 8 for the opening one-day international against Pakistan.
Sophia Gardens is then the host for Welsh Fire's matches in both the men's and women's Hundred which gets underway later that same month.