The Bluebirds want Mackay to replace Dave Jones, who was sacked last month following their play-off semi-final defeat by Reading.
An official approach was turned down by Watford but following discussions at boardroom level, chairman Graham Taylor said: 'We have reluctantly agreed to allow Malky to speak to Cardiff.'
Discussions: Mackay has been given the green light to speak Cardiff
City made their move after former England striker Alan Shearer revealed he had held 'unsuccessful' talks with the club earlier this week.
Ex-Celtic, Norwich and West Ham defender Mackay, 39, has been in charge at Vicarage Road for two seasons.
Watford were among the favourites to be relegated both years but Mackay guided them to 16th and 14th-placed finishes despite operating on a shoestring budget and regularly seeing his best players sold.
This summer he has already lost top scorer Danny Graham to Swansea while fellow striker Will Buckley was sold to Brighton.
The next step: Cardiff made it to the play-offs, but were beaten by Reading over two legs
Chief executive Julian Winter also left last week leaving new owner Laurence Bassini to run the club.
Bassini insisted yesterday the club would do 'everything in our power' to keep hold of Mackay, but the Scot has now asked permission to open talks with Cardiff.
Taylor added: 'The owner spoke with the board members and following Malky's request to speak to Cardiff, we have granted him permission.'
Mackay only signed a new three-year contract in March so Cardiff would have to come up with a compensation package if they can lure him away.
A statement from the Bluebirds read: 'Cardiff can confirm talks are under way with Malky Mackay to become our new manager.
'The talks began after permission was granted by Watford following our approach.'
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?Explore more:People: Graham Taylor, Danny Graham, Alan Shearer Places: Cardiff, Norwich, United Kingdom
Source: Daily Mail
Source: Daily Mail