The pair met at Holyrood on Tuesday.
The two MSPs thought to be in the running to replace Humza Yousaf held private talks on Tuesday, it has emerged.
John Swinney and Kate Forbes have both received support from senior members of the SNP since First Minister Humza Yousaf announced on Monday he would step down.
But with some in the party seemingly keen to avoid a similarly bruising leadership contest to the one which saw Mr Yousaf narrowly overcome Ms Forbes last year, she met with Mr Swinney at Holyrood on Tuesday.
A spokesman for Ms Forbes said on Wednesday: “We can confirm Kate spoke to John yesterday.
“It was a purely informal meeting. Kate is continuing to weigh up whether to run and is grateful for the growing outpouring of support.”
It is not yet clear what was discussed at the meeting or if any agreement was reached, but both MSPs – who occupied two of the highest profile jobs in Nicola Sturgeon’s administration – have said they are weighing up the opportunity to go for the top job.
Meanwhile, Ms Sturgeon urged anyone who does run to ensure any contest is “positive”.
Speaking to journalists in Holyrood, the former first minister said: “I’ll make up my own mind, I’m not going to tell other members how to vote.
“What I would say is that I hope the contest is positive, I hope it is forward-looking, and I hope it focuses on the things the SNP needs to do to continue it’s very strong election-winning streak.”
Asked if she is involved behind the scenes in the leadership race, given her former deputy and one of her closest political allies is in the frame, Ms Sturgeon, with a laugh, said: “No, I am not.
“I have spent almost my entire life in the thick of political drama and I’m actually quite enjoying not being in the thick of political drama anymore.”
Ms Sturgeon’s comments come after First Minister Humza Yousaf pushed for unity within the party.
He told the BBC earlier on Wednesday: “I would say to supporters of any candidate that we will gain nothing if we talk each other down.
“The only people who benefit from that are our opponents.”
But writing in the Scottish Daily Mail, former minister-turned-SNP rebel Fergus Ewing said Mr Swinney taking on the top job would see a “de facto” deal put in place with the Scottish Greens.
“The green tail has been allowed to wag the dog for too long,” he wrote.
“Last week, it was docked. But this week, it has re-emerged as a kind of phantom limb.”
