Speaking ahead of Marseille's Champions League Group F clash with Chelsea at Stamford Bridge on Tuesday, Deschamps said he had a "long meeting" with Liverpool officials before opting to stay in France.
"I don't think the fans or the club officials would have been very pleased if after two days back I was looking to join another club," he added.
Deschamps captained France to glory in both the 1998 World Cup and Euro 2000.
As a coach he took Monaco to the 2004 Champions League final and won the Serie B title with Juventus in 2006-07 after they had been demoted from the top flight following a wide-ranging investigation into match-fixing that had rocked Italian football.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.