There are three resolutions on the subject that could be debated at the party's policy convention in Montreal next weekend.
Two of the resolutions favour cooperation while a third opposes it.
Mulcair says he does not trust the Liberals and would not cooperate with them before, during or after an election.
But it's unclear whether they'll make it to the floor of the convention for a full debate because they aren't on the list of so-called priority resolutions. Priority resolutions are most likely to wind up actually being debated and voted upon.
There is also a non-priority resolution calling for NDP to withdraw from a host of free trade agreements, which flies in the face of Mulcair's call to keep an open mind on trade deals.
Another non-priority resolution calls for the party to develop a policy to permit doctor-assisted suicide for consenting adults who are terminally ill.
The priority resolutions are generally less likely to spark acrimonious debate
One that is to be presented on the party to adopt a code of conduct to guarantee "equitable and humane" treatment of campaign volunteers by party staff.
It says federal staff have in the past expressed confusion "over whether being nice to volunteers is a job requirement" during campaigns.
Since volunteers are not protected by collective agreements or compensated for their work, the resolution, proposed by New Democrats in Oshawa, Ont., says a code of conduct is needed to make sure they're treated fairly.
The resolution says the code should be drafted by a committee of volunteers; it should include a meaningful grievance procedure for those who feel they've not been treated nicely as well as disciplinary measures for staff who violate the code.
It calls on the party to have the code in place by the next federal campaign in 2015.
A number of priority resolutions are aimed at protecting the rights of workers and labour unions, a traditional NDP ally.
Others reflect the party's determination to maintain its newfound base in Quebec, which delivered 59 of its 75 seats to the NDP in the 2011 election, vaulting the party into official Opposition status for the first time in its history.
For instance, one resolution calls on the party to change the title of its national director back to the old title of "federal secretary" — out of deference to the fact that "the Canadian people includes the nation of Quebec and the First Nations."
Another calls for a review of the Broadcasting Act and legislation governing the national broadcast regulator "to take into account the different francophone and anglophone realities in the country, especially those of the Quebec market."
Another reaffirms NDP support for requiring all Supreme Court justices to be bilingual.
Likely the most controversial priority resolution will be a proposed new preamble to the NDP's constitution, which is aimed at softening the party's socialist edges.
The current preamble touts the merits of "democratic socialist principles," including the principle of "social ownership" and an economy geared to meeting the social and individual needs of people and "not to the making of profit."
The proposed new preamble makes only a glancing reference to the party's "social democratic and democratic socialist traditions" and takes a much more hands-off approach to the economy.
It affirms that government has a role to play in creating the conditions for sustainable prosperity" and should have the power to "address the limitations of the market" in advancing economic justice and protecting the environment.
The party has tried twice before the rewrite the opening lines of its constitution but rank and file New Democrats have balked.
Party members will have a chance to review resolution priority as the convention gets underway.