But Brumbies coach Jake White insists he will not pressure Australia's premier No 7 into a decision and is happy to wait until Pocock is ready to finalise his future.
Force skipper Pocock is off contract at the end of the Super Rugby season and White has contacted him to express his interest.
Pocock would be a perfect fit at the Brumbies after the two-time champions lost Michael Hooper to the Waratahs last week.
The Brumbies were blessed with Wallabies great Smith filling the No 7 duties for almost a decade, while Hooper is viewed as a future Wallaby.
Injured Brumby Colby Faingaa is also highly rated, but White said he would be ''crazy'' not to consider signing the Wallabies flank.
The former Springboks coach is also keen to use his South African contacts to help grow Pocock's charitable foundation, Eightytwenty Vision, which helps underprivileged people in rural Zimbabwe.
The chance to work closely with politicians in Canberra could also attract Pocock to the Brumbies.
But after a week of turmoil at the Force where the players voted to oust coach Richard Graham, White said the recruiting process was sensitive and ''there's no rush''.
''There's always going to be speculation about the top players … we have shown an interest in [Pocock] just like all other franchises have,'' White said.
''But there's no rush, the fact he would consider [joining the Brumbies] is fantastic.
''We want to become better and better and better every year, so if bringing him to the Brumbies would send a positive message and I'm sure it will add value to us.
''I respect the fact David doesn't want to rush into anything and I'm not going to put pressure on him.
''When the time is right we would be happy to offer him something if he's keen.''
The Brumbies' impressive start to the season will help them in their pursuit of Pocock.
They unexpectedly sit at the top of the Australian conference and will attempt to extend their lead when they play the Lions on Friday.
Pocock is the best player on the Force's roster and he is trying to lead the club through one of the most difficult periods in its history.
Graham was sacked last week after it was announced he had signed to become the Reds' coach for the next Super Rugby season.
The Force is keen to secure Pocock beyond the end of the year.
But after watching the Brumbies' new generation rapidly evolve into a strong team, Pocock could be keen to move to Canberra.
Pocock - who turned 24 on Monday - is the best No 7 in Australia and is considered one of the premier openside flanks in the world.
If he does decide to join the Brumbies, it would be a massive coup for a club which had a disastrous campaign last year.
White has put the Brumbies in a position where they are considered a chance of breaking their seven year finals drought.
Expectations for the young group are beginning to change and White was confident his team could handle the extra attention.
''It's nice for us that people are seeing us as a team that can win against tough oppositions,'' White said.
''Outsiders didn't think we would win a game this season so we don't think about that … every week the pressure is different.''