Neilson has been given the green light to bolster the threadbare squad after Hearts' year-long period in administration officially came to an end on Wednesday.
The transfer embargo handed out by the SPFL has been lifted and former club defender Neilson has told supporters to expect to see new recruits within the next fortnight.
Following last month's squad clear-out that was triggered by the appointment of Neilson and new director of football Craig Levein, the Tynecastle club have been left with only 13 recognised first team players.
And Neilson is well aware of the size of task facing him ahead of a Championship campaign that involves both Rangers and Hibs.
Hearts have already lost out on defender Darren McGregor to Rangers but have been linked with former Dundee United midfielder Morgaro Gomis, ex-Rangers goalkeeper Neil Alexander and striker James Keatings, who has turned down a new offer to stay at Premiership newcomers Hamilton.
Neilson admits he is now looking forward to strengthening a side that has been brought to its knee by the ravages of administration.
"It now means we can move forward, we are out of administration and we can start planning, and start taking the club in the right direction," he said. "We can start hopefully bringing players in to improve the team and to develop players. I don't want to give names just now for players we have not signed, we're in talks, in advanced talks with a lot of players and hopefully within the next week or two we'll start signing players up because that is the embargo lifted. It's been a long, hard year but it's time to look forward."
Asked if the foundations are in place for the club to regain their status as the third force in the Scottish game, Neilson said: "Definitely, the facilities are here, the people are here and it's just a case of moving on, developing and progressing as a team and as a club, and that's the target - to get back to where we belong.
"There has been no pressure put on me at all in terms of next season, we know our targets, we know what we need to do and know how we're going to do it. It's a case of developing players and winning games because ultimately that's what it's about, winning games and challenging to get ourselves back to where we belong."
Asked about fans' favourite Rudi Skacel, who is thought to have been offered a youth coaching role at the club, Neilson added: "It's an issue we need to deal with and need to speak about. Craig and I will deal with it, we've spoken to Rudi and it's not something we want to speak about just now. Rudi has been spoken to and he knows the situation."
Hearts, meanwhile, will start selling discounted season tickets from today. In phase 1 of the sale, an adult book ranges from £260 to £410, while under-12s can watch the team at home for as little as £45.