Edwards, whose contract with Wales expired at the end of the World Cup, left London Wasps by mutual consent yesterday and has been heavily linked with a position with England.
The Welsh Rugby Union have made it clear that they are desperate to keep Edwards on board but Gatland says the former rugby league hero must put himself first and not rush into anything when it comes to making a decision on his future.
"Shaun made it clear while he was out in New Zealand that he wanted a few weeks to reflect on things after the World Cup and I respect that," said Gatland, who previously coached alongside Edwards at Wasps before the duo began working with Wales in 2008.
"I was a bit surprised like everyone else that Shaun had finished with Wasps as he had been there for so long.
"The important thing now, being such a passionate man, is that he does what is best for Shaun Edwards. We go back a long way and we are good friends, but the important thing is that he does what's right for him."
Gatland, who signed a four-year contract extension with the Welsh Rugby Union that will take him beyond the 2015 World Cup in England, admits Edwards' future was not an area of concern Down Under.
The situation may have received plenty of column inches in the English and Welsh press but it wasn't a regular topic of conversation among the Wales coaching staff.
"He never spoke to me at all about Wasps and their situation. He is such a good professional that his focus was on Wales and the World Cup, and anything else was in the background," added Gatland.
"The reason Shaun and I have not spoken (since returning from New Zealand) is he made it clear that after the World Cup he wanted time to reflect. But it must have been in the back of his head, and it was very easy to make a hasty decision.
"We definitely didn't speak about it, he's a very private person and he keeps things to himself.
"I'm no different in that you've got to make a decision based on what's best for you and your family. Whatever we (Wales) may want, that is secondary to what is best for Shaun."