Candidates who wish to migrate to Quebec under family class must have a close relative willing to sponsor them and that relative must either be a Canadian citizen or a Canadian Permanent Resident resides in the province of Quebec.
You need to apply to be a sponsor before the application for selection certificate family class visa for any of your close relatives.
As a sponsor, you and your relative must meet certain requirements, like Federal sponsorship. The sponsor must submit sponsorship application to the government of Canada (Case Processing Centre).
If you are found eligible to sponsor, you must submit an undertaking application including an application by the sponsored person for quebec selection certificate for spouse to the government of Quebec. The
You can sponsor your family to Quebec in two different. One process is used for sponsoring your spouse, conjugal or common-law partner and/or dependent children.
A different process is used to sponsor other eligible relatives such as:
Sponsoring a spouse, partner or dependent child
Sponsoring other eligible relatives

Your spouse, common-law or conjugal partner, or dependent children (including children adopted by you prior to settling in Quebec) may be eligible to immigrate to Canada as permanent residents.
If you are a Canadian citizen or a permanent resident of Canada who has been living in Quebec can sponsor a spouse, common-law or conjugal partner, or dependent children
You can apply as a sponsor if your spouse, common-law or conjugal partner, or accompanying dependent children live with you in Quebec, even if they do not have legal status in Canada.

To be a sponsor, you must be 18 years of age or older.
A sponsorship agreement must be signed between you and the sponsored relative that commits you to provide financial support for your relative, on demand. The agreement also states that the dependent who will now become a permanent resident will make every effort to support her or himself.
You must provide financial support for a spouse, common-law or conjugal partner for three years from the date they become a permanent resident.
The sponsor is required to provide financial assistance for a dependent child either for 10 years, or until the child turns 25, whichever comes first.

signed a sponsorship agreement to sponsor another relative in the past but failed to provide financial support you agreed prior to this.
defaulted on a court-ordered support order, such as alimony or child support
received government financial assistance for reasons other than a disability
were found guilty of a violent criminal offence or any other offence against a relative or any sexual offence—depending on circumstances such as the nature of the offence, how long ago it occurred and whether a pardon was issued
defaulted on an immigration loan—late or missed payments
are in prison
have declared bankruptcy and have not been released from it yet or
you not be able to sponsor another person if you have previously sponsored relatives who later turned to the government for financial assistance.

The quebec spouse sponsorship program allows you to sponsor your spouse, de facto spouse or conjugal partner, provided any of the prior are 16 years of age.
The quebec sponsorship processing time and quebec spouse sponsorship processing time on an average is about 3 months including the csq family sponsorship processing time.

**Note: any other factors not included in this list might also make you ineligible to sponsor a relative.