The Los Angeles Galaxy forward saw his stock rise after a highly successful loan spell with Everton earlier in the year, before flourishing at the World Cup in South Africa.
Manchester City boss Roberto Mancini has expressed his interest in the player and Everton are also keen to secure a permanent move for the 28-year-old striker.
And Harkes - the first American to play in the Premier League - has urged his countryman to prove himself while he is at the peak of his game.
"I think if the opportunity presents itself he should go," Harkes said.
"Obviously it depends on what he wants as an individual but if the opportunity presents itself for him to take that challenge he needs to do it now - to really commit to playing overseas and do it for a longer period of time, which is better than doing it in the short-term, like he did with Everton.
"It was a successful and fantastic experience, but he needs to do it over a longer period of time.
"That's when you get challenged in more ways, so if it's there I think he should grasp the opportunity and go for it."
While Donovan may leave Major League Soccer for pastures new, Harkes hailed New York Red Bulls' move for Thierry Henry.
Harkes, who spent a spell as Red Bulls' assistant manager, said the former Arsenal striker can help take the sport to "the next level" in the United States while providing fresh impetus to the league and his new team.
"I think Henry's signing is huge to MLS," said the former Sheffield Wednesday and Derby midfielder. "The league itself is starting to stabilise.
"In terms of it being a business, you need to be able to bring in quality players that are going to be able to take your team to the highest level.
"To do that you need to bring in players like Henry, which are internationally recognisable and still have a lot to offer.
"Henry is a quality player who comes into the Red Bulls set-up and can be just the injection that they need to raise not only the awareness and the interest, but to take the game to another level."