Veolia ES (UK) and Enterprise Managed Services are both bidding for the contract, which will include grounds maintenance and cleaning across all Brent parks, cemeteries, open spaces and social housing estates.
However, a group of local residents in Brent has been running a Bin Veolia in Brent campaign since March, accusing Veolia of "grave misconduct" by working in illegal Israeli settlements on Palestinian land.
The campaign is part of a larger international movement against French parent company Veolia Environment for the same reason.
About 40 Bin Veolia in Brent campaigners gathered outside the new £90m Brent Civic Centre in Wembley last week to hand a petition to the council's executive.
The petition, which was signed by hundreds of local residents, urges council bosses not to consider the Veolia bid.
Veolia currently holds the seven-year-contract, due to end in April, to provide recycling and refuse collections as well as street cleansing.
A council spokesman said: "Brent is currently in the middle of its procurement exercise and so cannot take into account any external factors that would jeopardise this process."
He added: "The council has received legal advice that, among other things, there are no grounds for excluding Veolia ES (UK) from the current procurement of the public realm contract on the basis of 'grave professional misconduct' in accordance with regulation 23(4)(e) of the Public Contracts Regulations 2006."