For selling a primary residence, there is not a time frame that you must buy another home in order to save money on taxes.
For your primary residence, you would calculate a gain or a loss on the sale of the home. A loss on your primary residence is not tax deductible. Any gain on the sale could be subject to capital gains treatment, unless you meet the rules for a "Section 121 Exclusion", which could exclude up to $250,000 ($500,000 married filing jointly) of gain from being taxed on your federal tax return.
In general, to qualify for the Section 121 exclusion, you must meet the ownership test and the use test. You are eligible for the exclusion if you have owed and used your home as your main home for at lest two years out of the last five years. Note you are not eligible for the exclusion if you excluded the gain from the sale of another home during the two years prior to the sale of this home. Complete eligibility requirements, limitations on the exclusion amount, and exceptions to the two year rule can be found in IRS Publication 523, located at this link: IRS Publication 523: Selling Your Home
So, if it has been your primary residence and you meet the ownership and use tests, you can qualify to exclude a gain up to those amounts from your income - regardless of whether you purchase another home at any point of time or not.
Note, if you were referring to a business or investment real property instead of your primary residence, in that situation there may be tax benefits of deferring a gain if the transaction were structured as a Like Kind Exchange, which does have a specific time frame on identifying and acquiring the other property.
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