Preston have eased their goalkeeper troubles by signing Sunderland's Jordan Pickford on a season-long loan.
Hearts have completed the signing of Nigeria international Juwon Oshaniwa.
Caley Thistle are on the lookout for a new manager after Terry Butcher quit to take over at Scottish Premiership rivals Hibernian.
Robertson - who has been coaching with former club Hearts - was manager of Inverness between 2002 and 2004 and guided them into the top flight for the first time in the club's history, as well as winning the Challenge Cup.
Asked if he would be interested in a return, he told STV's website: "Absolutely. I've had success there in the past with the championship and the cup win and a couple of semi-finals as well.
"Kenny Cameron, the chairman, and Graeme Bennett, the director of football, have got a fantastic record of picking managers and I'm sure they'll get this right as well.
"Where Terry leaves the club - in second place and the semi-final of the League Cup with a tremendous squad of players - means it has suddenly become an attractive job.
"A lot of people possibly wouldn't have looked at it in years gone past but now they see the team doing well with a really strong squad of players playing an attacking brand of football.
"It is a tough area to relocate to and have to commit to there but if you do, you are in for a treat because it is a wonderful place to live with wonderful people.
"More importantly from a football perspective, you are picking up a very good side."