Pulis quit on Thursday night – just two days before the start of the new season – following crisis talks with co-chairman Steve Parish, leaving Palace searching for a successor.
Mackay, who took Cardiff into the Premier League before being sacked last December, told Sky Sports News HQ earlier this week that he was looking to get back into management – with the right club.
"At the moment I’m just waiting," he said. "I had a couple of opportunities in the summer that I didn't feel I was ready for.
"So it's really just a question of wait and see – but I really want to get back into it and manage again.
"I really enjoyed the challenge of coaching against some of the top coaches in the world and pitting your wits against them.
"Everyone would love to manage in the Premier League – but there are only so many clubs – I certainly enjoyed it last year and I would love to have the chance to manage there again."
If Mackay joins Crystal Palace, he will be reunited with his former head of recruitment at Cardiff - Iain Moody.
Moody was appointed sporting director at Selhurst Park last year after also being sacked by Cardiff, and he had previously worked alongside Mackay at Watford.
Sky Bet have slashed the odds on Crystal Palace being relegated following the departure of Pulis.
The former Stoke boss oversaw a remarkable turnaround after being appointed in November, defying odds of 1/20 for relegation to lead them to an 11th-place finish.
Sky Bet football trader Jamie Munro said: "Crystal Palace looked doomed when Pulis took charge last season and with little improvement to the squad we fear for them again now.
"We started to see backing for Tony Pulis to be the first manager to go on Thursday morning, which came as a major shock as he was initially a 40/1 outsider in the market, which has been followed by money on the Eagles to be relegated."
Palace have been linked with a move to bring their former winger Wilfried Zaha back to Selhurst Park after a difficult first year at Manchester United.
Speaking to Sky Sports News on Tuesday, Parish insisted that Pulis would be given all the support he needed to build the squad he wants.
"It's up to the manager, the players we sign. It's not up to me. I'm there to help him get the squad he wants," Parish said.
"There's a sentimental value and I loved Wilf as a kid and he did sensational things for us.
"I know the fans would like him back and that will play a part, but in the end the manager will decide what we do."
There has been surprise on social media to Pulis' Palace exit with West Ham co-owner David Gold tweeting: "Tony Pulis leaves Crystal Palace only hours before the start of the season. Hard to believe."
QPR defender Rio Ferdinand added: "Wow. Tony Pulis gone... management swings and roundabouts started earlier" while Tony Pulis' son Anthony - a player in the Major Soccer League - tweeted "right I'm off to get the guest room ready."
Watch Crystal Palace face Arsenal in the Premier League live on Sky Sports 1 HD on Saturday. The programme starts at 4:45pm.