Mackay was sacked in December after a series of disagreements relating to the Bluebirds' summer transfer business.
The club surprisingly decided to again raise the issue on Thursday by releasing a statement in which chief executive Simon Lim again criticised Mackay, particularly the signing of striker Andreas Cornelius, which Lim claimed cost the club in excess of £8.5million.
Cornelius returned to FC Copenhagen in January and scored a hat-trick on his second debut for the club.
The League Managers' Association chief executive Richard Bevan responded by claiming Mackay had to report to Lim "in respect of all matters pertaining to the transfer of players".
The statement by Lim did however, praise Solskjaer's work in the January transfer window, but the Norwegian did not want to offer his thoughts on Mackay.
"It is early doors for me and it is encouraging they are happy with what I have done but what happened in the past is not for me," he said.
"It guides what resources they give me and what remit I have
I'm just running the club as I would like to.
"It's not got anything to do with me, what happened before
I am just focused on my team because the January window was chaotic."
On the pitch, Cardiff prepare to face holders Wigan in Saturday's FA Cup fifth-round tie.
Latics were relegated from the Premier League last season, just days after completing cup success over Manchester City and, with Cardiff currently in the relegation zone, Solskjaer hopes the Welsh club do not follow Wigan's lead.
"They proved last season what the FA Cup was all about, a chance for smaller clubs to win trophies," he said.
"I would like to go one better than they did and win the cup and stay up, but in any way, shape or form, if you play in a cup game you want to win it.
"It's a chance for some players to come in and show they should be playing in the league and I do not go into any game hoping we lose."
Kenwyne Jones and Fabio are cup-tied.
The Bluebirds are waiting for United to confirm Wilfried Zaha's availability; the winger was an unused substitute in the Red Devils' third-round defeat to Swansea.
Spanish defender Juan Cala will make his debut while Solskjaer may opt to hand starts to the Norwegian trio of Magnus Wolff Eikrem, Mats Moller Daehli and Jo Inge Berget
Craig Bellamy is suspended.
Wigan defender Ivan Ramis will be out to show Cardiff what they are missing this weekend.
The 29-year-old centre-back was all set to complete a transfer to Ole Gunnar Solskjaer's men, who had met Latics' asking price, before the deal fell through with injury concerns appearing to dissuade the Bluebirds.
Ramis has featured just seven times in 13 months due to a knee injury and a soft-tissue problem but has now returned to full training and could make his comeback in the fifth round at the Cardiff City Stadium.
Like boss Uwe Rosler and many of the current Wigan squad, the Spaniard played no part in the glorious FA Cup campaign which culminated in a memorable May victory over Manchester City at Wembley, but the manager suggested Ramis could draw upon another source of inspiration.
"Who wants to play against Cardiff? One of them desperately wants to play to prove them wrong and it's not Nicky Maynard because he is cup-tied," said Rosler.
On-loan Maynard does not have permission to play against his parent club, while defender Rob Kiernan and forward Martyn Waghorn are also unavailable as they are cup-tied.
Midfielder James McArthur has been struggling with illness and will not travel with the squad to south Wales, while top scorer Nick Powell has not played since January because of a hamstring problem.
Source : PA
Source: PA