"Even though I would agree that you are looking for businesses for the future that are internet based where there can be high rates of growth, I would suggest that this one has probably seen its best days now," Mr Cox said.
"Therefore if they can get what they feel to be a very good price for it then definitely they should consider selling it."
Mr Cox ran unsuccessfully for a seat on the Fairfax board at November's annual general meeting.
Fairfax bought Trade Me for $700 million in 2006 and floated 34 per cent of the company in December 2011 through an initial public offering which raised $363 million.
It sold a further 15 per cent in June 2012 for $206 million.
Fairfax's full-year accounts said Trade Me had a "somewhat variable performance" over the second half of 2011/12.
The mooted sale would give Fairfax the opportunity to bolster its balance sheet - the company's net debt stood at $1.14 billion at June 30, 2012.
Mr Cox said $811 million from the Trade Me sale would "put a nice dent in the debt at Fairfax".
"It also puts them in the position where if there came an opportunity for what they considered to be a good investment, they would have the funding ability from which to invest in something," Mr Cox said.
"If you have a lot of debt on your balance sheet, you are bit handcuffed because you can't move very quickly, you can't take opportunities," Wealth Within analyst Dale Gillham said on Sunday.
"In the last few years analysts have been looking down at companies with higher debt levels and so therefore reducing debt is what they like to see."
In 2012, Fairfax announced 1,900 job cuts, closure of printing presses in Sydney and Melbourne and the creation of online paywalls in a bid to deal with the structural shifts in the media industry.
A Fairfax Media spokesman said on Sunday the company had no comment.
-AAP
