The lease from Cardiff Athletic Club ends in January 2022 and the region wants a long-term extension so it can redevelop the city centre site.
It wants 15,000-seater stadium with a retractable pitch and sliding roof so it can be used as a concert venue.
Blues chief Richard Holland says talks have taken place for some time.
"We are in the final stages of completing that negotiation and I am hopeful we can call an EGM (emergency general meeting) for January for the athletic club to get them to ratify what is a memorandum of understanding.
"I very much hope the members will ratify that an EGM."
Any regeneration at the Arms Park site would add to the redevelopment of that area of Cardiff with the Central Square project next to Cardiff Central Station and the plans to transform the Brains Brewery site.
But Mr Holland said: "Let's get the agreement secured and I am hoping to do that in the not too distant future at an EGM in January.
"The future from there on in would be very exciting for everybody involved at Cardiff Athletic Club, Cardiff RFC and Cardiff Blues.
"Not only have we got only four or five years at the Arms Park but and I am hopeful we can extend that out to a 150-year lease.
"Built into that would be a development opportunity where we could put a new stadium or put in a subsequent development into the Arms Park that will be a fantastic thing for Cardiff Blues, Cardiff Rugby and the city of Cardiff.
"If we could achieve that it would be a brilliant legacy for future generations and the future of Welsh rugby."
Cardiff Blues rugby region want to extend its lease on the Arms Park to rebuild the stadium as well as build an exhibition centre, a hotel and flats.