Todd, 35, was sacked by the Spitfires in September after 11 months in charge, having previously played alongside Nicholson for Torquay from 2007-2010.
"Why wouldn't I pick his brains," Nicholson said.
"It's a chance for me to have a chat with him and see what he's learned over the past year in management."
Todd was appointed player-boss of Eastleigh last October, but was sacked just four games into this season.
"It's a chance for him to work on a bit of fitness and make sure he keeps his eye in," added Nicholson, who is celebrating a year as Torquay manager.
"He had a couple of years as an assistant as well, so it's a chance for another learning curve for me.
"What can he tell me that I didn't know, what can he put forward that maybe I hadn't thought about, and it's been nice having him around."
Todd played more than 150 games for Exeter City before moving to Plainmoor in 2007 and playing 78 matches for the Gulls.
"I want to get back into football," Todd told BBC Sport.
"If there's an opportunity as a manager around, and it suits me, I'd love to do it again. I learned a lot in the eight months I was in charge of Eastleigh.
"But I would be inclined to do something else, be that playing, a coach or assistant manager.
"I've got a few irons in the fire and I'm just waiting on a few things."
But Nicholson does not believe that Todd would choose to return to Plainmoor as a player.
"He's had a year as a manager now and once you've had the taste of that you don't necessarily want to go back to just being that player," he added.
"He's got his own things on the go and I hope he gets the opportunities sooner rather than later, but if I can help him in the meantime I will."
Torquay United manager Kevin Nicholson says he is taking the chance to learn from former Eastleigh boss Chris Todd, who is training with the club.