The 20-tonne granite carving by Edinburgh sculptor Ronald Rae has proved a big hit with tourists and local people alike since going on show as part of an exhibition in Holyrood Park nearly two years ago.
More than 2000 people signed a petition calling for the lion to be made a permanent feature, but the parliament's art advisory group repeatedly rejected the pleas.
Most of Mr Rae's other sculptures which were on display in the park have now been moved and the temporary reprieve granted to the lion was due to run out in four weeks.
But now the art advisory group and the cross-party Scottish Parliamentary Corporate Body (SPCB) have agreed to enter discussions with Mr Rae on his offer of a long-term loan.
And Historic Scotland, which runs Holyrood Park, is expected to agree the sculpture can remain at its present site opposite the front of the parliament.
The SPCB, however, said the lion would not become part of its permanent art collection and insisted the arrangement to keep it at Holyrood was only for three years.
A parliament spokeswoman said: "The SPCB remains of the view that the Ronald Rae lion sculpture does not meet the criteria for incorporation as part of its permanent collection of art works. It will not therefore be exhibited on the parliament's grounds.
"However, the SPCB has agreed to explore the possibility of entering into loan agreement negotiations with the artist which could enable the lion to stay in its current location in Holyrood Park for up to three years.
"This temporary arrangement is a practical solution by the SPCB to help accommodate some of the public interest in experiencing the sculpture until a permanent home in another location is found."
Doreen Grove, Historic Scotland head of understanding and access, said: "If the parliament wishes to accept the loan of the lion sculpture we will be happy to find an appropriate way to accommodate its wishes.
"Our understanding is that such a loan would be on a fixed-term basis, after which it will be moved to a new location. The details of how the loan will be managed have still to be agreed."
Pauline MacDonald, Mr Rae's administrator, welcomed the SPCB decision and said that he would be happy to negotiate an agreement.
And she said although the original idea had been to move the lion across the road on to the parliament's land, it was probably better staying at its current site. She said: " A lot of people feel it is perfect where it is. We are happy with that."