The three sides had hoped to have a deal by Monday.
Aimia announced earlier this month that TD (TSX:TD) will take over from CIBC as its main banking partner.
However, the company which operates the Aeroplan points system said at the time that it was possible both TD and CIBC would offer cards with Aeroplan rewards points starting next year if they could come up with an agreement.
TD said Monday that they were discussing "a framework that would see CIBC retain cards held by their franchise banking customers, which are about half the portfolio, and TD acquire the remainder."
CIBC has partnered with Aeroplan for more than 20 years but its current 10-year term agreement with Aimia ends this year.
The bank declined to match an offer from TD, but has proposed it keep half of current Aerogold customers who have other products with CIBC that earn Aeroplan miles, such as chequing accounts and mortgages.
Montreal-based Aimia, which began as division within Air Canada that managed frequent fliers points, has since expanded to handle other customer loyalty programs in various industries in several countries.