When he arrived at Ashton Gate the Robins were 22nd in the table, two points from safety, after winning only four of their opening 26 league games.
“We have to focus on getting the point need – that’s absolutely paramount,” Ashton told BBC Points West.
“We’re in the middle of identifying talent for next season and I would like to get as much of our business done as early as possible to give Lee Johnson and the players a full pre-season.
“He knows what he wants but identifying who is always the most challenging part. We are working to a strict DNA – the technical, the physical, the tactical, the psychological and, importantly, the financial fit for the club.
“We will not leave any stone unturned in our efforts to find the right players.”
Will Lee Tomlin return?
On-loan Bournemouth midfielder Lee Tomlin has had a major influence since arriving at Ashton Gate in January, with four of his five goals coming in his last seven appearances.
Ashton admits finalising a deal to get him back with the Robins is firmly on his radar.
“I’m too long in the tooth to say ‘never’,” said Ashton. “We are having on-going discussions with Lee.
“He’s happy and a happy player plays well – he’s done extremely well for us.”
City go to Blackburn on Saturday before their final home game of the campaign against Huddersfield and a last-day trip to Queens Park Rangers.