AltAssets reported two months ago that the business had filed to list on the public markets, although no figure was given at the time.
La Quinta, which currently operates 830 hotels, was acquired by Blackstone in a $3.4bn take-private deal in 2006.
Earlier last year it was reported that Blackstone was looking to sell La Quinta for as much as $4.5bn, and that the company had attracted interest from Choice Hotels International and private equity firms.
In December global hotel company Hilton Worldwide, which was acquired by the Blackstone Group at the height of the buyout boom, raised $2.35bn in its public listing.
Shares were priced at $20 apiece, at the upper end of its $18 to $21 range, giving the company a valuation of almost $20bn.
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