Counsel for the musician confirmed he will seek leave to appeal against the decision reached in actions related to the handling of Covid restrictions in Northern Ireland.
Mr Swann issued defamation proceedings after Sir Van chanted that he was “very dangerous” during a dinner at Belfast’s Europa Hotel in June last year.
It came after gigs by the singer-songwriter at the venue were cancelled due to a ban on live music imposed as part of coronavirus restrictions.
He took to the stage and directed criticism at the health minister, with DUP MP Ian Paisley invited up from the audience to join the chants.
Video footage of the incident subsequently went viral.
Mr Paisley later defended his involvement as an act of parody, comedy, banter and sarcasm.
The defamation claim also cites further incidents involving a media interview and online video.
In a separate action, Sir Van is suing Mr Swann and the Department of Health over an opinion piece he wrote for Rolling Stone magazine.
The article, published after the performer released anti-lockdown songs, expressed disappointment at someone he acknowledged as “one of the greatest music legends of the past 50 years”.
He described the songs as a “smear” on those involved in the public health response to the pandemic.
During a hearing at the High Court in June this year, lawyers on both sides set out opposing arguments on how the two related actions should proceed.
Mr Swann’s legal team sought trial by a judge sitting alone, while Sir Van’s representatives pressed for the claims to be determined by a jury.
Points were also raised about the complexity of the issues involved, and the potential for delay in securing a courtroom.
Following deliberation, Mr Justice McAlinden held that both actions should be heard by a judge alone.
Sir Van’s legal representatives attended the Court of Appeal yesterday as part of plans to seek leave to challenge that ruling.
Barrister Peter Hopkins said permission is required before the notice of appeal can be served.
With the trial on hold until the jury issue is finally determined, Lady Chief Justice Dame Siobhan Keegan listed the challenge for a preliminary hearing next month.
She said: “I will set a date for the leave application, for a one-hour (hearing).”