In a statement released on Saturday, Green leader Elizabeth May says such co-operation would rally the progressive vote behind the Liberals and encourage proportional representation.
In a news release, Liberal leadership candidate Joyce Murray claims she orchestrated the bid to elect a Grit, saying she called May and asked her not to run a candidate in the Labrador byelection.
In 2011, Liberal Todd Russell lost to Penashue by 79 votes.
Penashue quit his post earlier this month after Elections Canada found his election campaign had accepted 28 different ineligible donations.
He has since pledged to run in a byelection, and is being supported by the prime minister, even though Elections Canada is continuing to investigate.
Elections Canada documents show that almost $48,000 in improper donations have been repaid to the federal Receiver General.
Earlier this week, Prime Minister Stephen Harper led a spirited defence of the ex-intergovernmental affairs minister in the House of Commons.
Also on HuffPost