Summer signings will be crucial for the Saddlers ahead of the new season after they released eight players last month.
Matt Taylor officially started as boss this week but Fullarton has revealed the pair have already started their recruitment drive.
He said: “We’re working hard. There’s a time and place to reveal what we’re doing and how we’re doing it because it’s a competitive market.
“Let’s just say the process is well and truly underway and as Matt’s mentioned, the amount of calls and contact that we’re having on a regular daily basis – it’s seven days a week.
“Even though Matt’s officially started on June 1, he’s been dual-rolling to make sure we’re ahead of the cuff.
“Looking for no different to what I said about Matt’s appointment.
“He was our first choice, the leading candidate and we’re delighted to get him. That’s the plan, the aim and drive regarding players also, position specific.”