United is still suffering the effects of the September 11 2001 terrorist attacks, which caused a downturn in the travel industry.
The airline reduced media expenditure to $57.3m last year from $78.4m in 2000, according to figures from Taylor Nelson Sofres CMR.
Reports in the US suggest that United wants to appoint a media agency closer to its Chicago-based headquarters, according to the Chicago Tribune.
If that is the case, the obvious choice would be Bcom3's Starcom Mediavest Group, now part of Publicis Groupe. However, Starcom already holds the account for Delta Airlines.
Zenith Media is part of Zenith Optimedia Group, which is owned by UK-based advertising network Cordiant Communications and France's Publicis.
Zenith was appointed to the business alongside Fallon in January 2001 when the business was said to be worth $120m after a pitch against the incumbent agency, The Media Edge.
The news marked a review for the airline out of the WPP-owned Young & Rubicam, which was the creative incumbent at the time.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .