26-year-old Hamilton's career is now handled by pop star manager Simon Fuller, who instructed the Briton to hand over a business card to Red Bull's Christian Horner a few weeks ago in Canada.
Amid the ensuing speculation and all the talk about Hamilton's current focus and criticism, his father Anthony - who now manages promising Force India rookie Paul di Resta - said he would advise his son to stick with McLaren.
"It's just something is missing and they'll find it," he told the BBC Sportsweek programme.
"They're going through a little bit of turmoil like you do in any relationship, but it is going to be a happy marriage, I believe, if he stays.
"As a formula one driver, Lewis has an opportunity to bring everybody together rather than let them fall apart."