New Zealander Gatland, 44, has revived Wales after a dismal World Cup, and he insists he will remain focused on that job should a Lions position come along.
Gatland told BBC Radio Five Live: "If there's a chance to get involved at some level that would be a huge honour but I have to make sure I don't neglect Wales.
"I'm not going to get ahead of myself - in the past other coaches have been involved with the Lions and haven't made their own job with their own nation the number one priority.
"The Lions take up a lot of time and there's a lot of politics involved in picking the right team."
Gatland and Edwards have enjoyed a hugely successful partnership having previously guided Wasps to Guinness Premiership and Heineken Cup glory.
Edwards, who is still head coach at Wasps, linked up with Wales to pursue a career in international coaching.
He turned down a role with England's second-string Saxons side to work at the elite level with Wales.
Gatland added: "I'd love Shaun to be involved and he would relish that responsibility.
"He's a very proud Englishman who's working for Wales at the moment and we're delighted to have him."
Edwards too has said the possibility of working alongside Gatland with the Lions is an exciting one.
The Wigan rugby league legend told the BBC's Inside Sport programme: "I think Warren would definitely go if asked and I'm sure he'd do a very good job.
"I'd like to put my hat in the ring - but not as a head coach."