Short answer. Yes. Article 913 of the Civil Code provides that if the heirs or devisees entitled to the preference decline to use it, any other heir or devisee who did not originally have that right may exercise it instead. Only if that heir also declines does the property go to public auction at any interested party's request.
What the law says
If the heirs or devisees do not choose to avail themselves of the right granted by the preceding article, any heir or devisee who did not have such right may exercise it
Civil Code, Article 913 — Auction If Right Unused. Read the full provision →
What the law says
should the latter not make use of it, the property shall be sold at public auction at the instance of any one of the interested parties
Civil Code, Article 913 — Auction If Right Unused. Read the full provision →
Other heirs get a turn before the property goes to auction
Article 913 answers this directly. When the heirs who hold the preferential right decline to use it, the door does not close on the estate: if the heirs or devisees do not choose to avail themselves of the right granted by the preceding article, any heir or devisee who did not have such right may exercise it. So yes, another heir, one who was not part of the original preferred group, can step in and claim the indivisible property before it ever reaches public auction.
The order the article sets up
The article establishes a sequence rather than a single all-or-nothing choice. First, the heirs or devisees given the preferential right decide whether to use it. If they decline, the right passes to any other heir or devisee who did not originally have it. Only when that second opportunity is also declined does the article move to its last step, and that step is public auction, not an earlier stage in the process.
Auction is the fallback, not the default
The article makes public auction conditional on both opportunities being passed up: should the latter not make use of it, the property shall be sold at public auction at the instance of any one of the interested parties. Auction only happens once neither the originally preferred heirs nor any other heir has stepped forward to take the property. It is not something that can be forced while another heir still wants to claim it.
What this means for your situation
Since the heir with the first right does not want the property, Article 913 gives you, as another heir, the chance to claim it before any auction takes place. Public auction is only triggered if you and any other interested heir also decline to make use of that opportunity. Until that second stage plays out, the property is not yet at the point where it must be sold at auction.