Villa manager Steven Gerrard is keen to bolster his squad and missed out on Rodrigo Bentancur in January, who chose to join Tottenham Hotspur from Juventus.
The Times report next on the agenda is Phillips, who has been identified as a key target.
Phillips has been limited to 12 Premier League appearances this season due to injury and his last came on December 5 against Brentford.
The 26-year-old is a full England international and one of Leeds' most important players.
Villa are prepared to smash their transfer record and offer Phillips wages totalling £10 million-per-year.
Their current record signing is Emiliano Buendia, who cost £34 million from Norwich City last summer.
West Ham United and Newcastle United have registered an interest in Phillips but it's believed Villa are ahead of other suitors.
Manchester United have been mooted in the past, but Phillips' love for Leeds would make a transfer to their bitter rivals nigh on impossible.
Phillips was named on the bench in Friday's dramatic 3-2 victory over Wolverhampton Wanderers.
He didn't end up coming on as Jesse Marsch's side took another vital step towards Premier League safety.
Jonny opened the scoring in the 26th minute before Francisco Trincao opened his Wolves account in the 11th minute of stoppage time.
The game changed shortly after halftime however as Raul Jimenez was sent off.
Jimenez was already on a booking and collided with Leeds goalkeeper Illan Meslier while chasing a loose ball outside his area.
With Wolves down to 10 men, Leeds launched a stunning comeback just past the hour mark as Jack Harrison bundled the ball home.
They were level three minutes later after Rodrigo smashed home a Dan James effort which had come back off the post.
Luke Ayling popped up in injury time to volley home from close range and move Leeds up to 16th and seven points clear of the drop.
It's their second late win in a row after snatching a 2-1 victory against Norwich City last weekend.
Marsch was asked about Phillips being on the bench at full-time by Jamie Carragher and Gary Neville and his response left the duo in a fit of laughter.
When asked about bringing him on, Marsch replied: "No. To be honest with you guys he was never going to play!"
He then elaborated: "We have injuries with a lot of our U23s guys from the Manchester United match in midweek, so we didn't have many players to put in the roster. Having Kalvin with the team, I think, was great, and even on the bench, he was fantastic."
Featured Image Credit: Alamy
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