The general issue of what exactly a "species" is has been addressed numerous times here, in different forms. Some good answers can be found at:
Defining "species" (Are species an emergent property or an ensemble of quantitative differences?)
How could humans have interbred with Neanderthals if we're a different species?
When has an organism evolved enough to be called a new species?
and a so far unanswered question:
References for historical momentum in asexual species definitions
I think Remi.b's answer that says:
The concepts of lineage and clade / monophyletic group are much more helpful. IMO, the only usefulness of this poorly defined concept that is the "species" is to have a common vocabulary for naming lineages.
is the place to start. A virus "species" is just a label to a lineage at one point in time. When we discover separate lineages of a virus, historically they have gotten a new label. It's then possible follow the lineages from there into strains/substrains, etc.
SARS-CoV-2 was first identified as the cause of a novel illness with a placeholder name 2019-nCoV. Its relation to the earlier SARS-CoV lineage was quickly identified and it's now been grouped alongside SARS-CoV-1 as a strain of the SARS-CoV species. So, given that SARS-CoV-1 and SARS-CoV-2 are considered strains of the same species, it seems highly unlikely that any variants of SARS-CoV-2 will be known as their own species any time soon.
One could consider other virus lineages as well. Influenza A is a species whose subtypes are described by two antigens, H and N, giving the perhaps somewhat familiar naming convention like "H1N1" or "H3N2". Each of these has contained different lineages often named by those causing illness in humans or animals, but at no time have these been considered separate species, they are all still considered the same species Influenza A.
The naming conventions for influenza A are pretty solid from long-term study and following precedent. The International Committee on Taxonomy of Viruses sets some conventions for naming, but their principles are:
To avoid or reject the use of names which might cause error or confusion
To avoid the unnecessary creation of names
None of these attempt to put any standardized distance between what are considered "different" versus the "same" species across different lineages. The ICTV code says this in vague terms, bold mine:
The criteria by which different species within a genus are distinguished shall be established by the appropriate Study Group. These criteria may include, but are not limited to, natural and experimental host range, cell and tissue tropism, pathogenicity, vector specificity, antigenicity, and the degree of relatedness of their genomes or genes. The criteria used should be published in the relevant section of the ICTV Report and reviewed periodically by the appropriate Study Group.
So, different study groups choose which criteria to use, and these need not be the same criteria each time. Introducing any would likely result in this situation. Instead, we have a fairly ad-hoc system given there is no particular biological meaning to "species" except as a lineage label, and this system is governed as much by scientific history as by any set level of genetic similarity. In the interest of maintaining stability, it seems unlikely that new virus species will be recognized under existing known virus species without novel discovery.