Warner Bros UK president and MD Josh Berger is also believed to be in the running, according to media reports.
They are among the names expected to appear on the shortlist being considered to take over from Andy Duncan who will leave the broadcaster at the end of the year.
They join other potential candidates that have already been touted including ITV director of TV, channels and online Peter Fincham, UKTV chief executive David Abraham, Microsoft UK MD Ashley Highfield,former BBC2 controller and Discovery Channel US chief Jane Root and internally, Channel 4’s director of television and content Kevin Lygo.
The search is being led by the broadcaster’s outgoing chairman Luke Johnson. He has enlisted executive recruitment company Egon Zehnder to start the process.
Fairbairn joined ITV in 2007 and has previously worked at the BBC as director of strategy.
Thomson has held various roles at the BBC including director of policy and legal, and director of strategy. She previously worked at Channel 4 as commissioning editor, science finance and industry in 1984.
Meanwhile, Berger was promoted to his role as UK and Ireland president and MD at Warner Bros Entertainment (WBEUK) in December 2006 after having worked with the media company for 17 years.
Prior to this promotion, Berger served as executive VP and managing director, WBEUK. He has also previously been senior VP and managing director for Europe, Middle East, and Africa, Warner Bros. International Television Distribution.