While he declined to endorse a candidate, Sarwar warned the contenders and their teams against infighting as the race becomes more embittered.
He told Forde: “I think genuinely the three people who are standing, I’ve got a lot of time for,” he said.
“I think they are able, talented individuals.
“The only (thing) that I would say to all three of them and to all 17 MSPs is your relationship with each other, your ability to work with each other and to look out for each other is going to be crucial.
“So, yes, go through a full leadership election, but think about what happens the day after it, not just what happens during it.”
Lennon – who has yet to secure enough support to get on the ballot of members – earlier said the leadership race was about finding “our party’s missing soul”.
She lost her seat at the election but is able to return to Holyrood after the summer recess to fill the Glasgow list MSP vacancy left by Sarwar.
Writing in the Sunday Mail newspaper, external, Lennon said: “Again, our political conversation turns inward as politicians and activists search through the rubble, trying to locate our party’s missing soul.”
She added: “Having lost sight of our roots, we struggle to place ourselves in Scotland’s future.
“It’s the worst of both worlds, but this identity crisis needn’t be the end of our story.
“People still need us, and we need them.”
The party’s ruling body, the Scottish Executive Committee, said a new leader would be in place by its conference on 19 September.
Nominations formally opened for two weeks on Monday 3 August.
Party members and supporters will be balloted on the leadership race from 28 August until 17 September.