“We will have a budget from £20m to £30m to £40m to £50m,” he said.
“It depends when we have the coach around the table.”
Villa finished bottom of the Premier League with 17 points and will play in the second tier of English football next season for the first time since 1987-88.
Xia, who will become chairman at Villa Park once the move is ratified, said the whole package to buy the club had cost him “over £100m”.
He said a new manager to replace Remi Garde, who left in March, will be named within two weeks.
Di Matteo is among the candidates, having had experience of winning promotion from the Championship with West Brom and overseeing Chelsea’s Champions League final victory in 2012.
“Roberto was one of the choices. He has been very good in the Championship and he did very well in the Premier League,” Xia told the BBC.
“We have other good choices. I think we will get the right one in two weeks.
“I think there is a lot of potential for Villa to be promoted very soon. They have a very good academy and facilities and a very good fanbase, which can attract a lot of people.
“If we can get the right team to work with we can get on the right track and I hope we can achieve it one year.”
‘Exciting times for Aston Villa’
Aston Villa chairman Steve Hollis, who also suggested British managers with Championship experience feature on the shortlist, is confident Xia’s success as a businessman bodes well for the future of the club.
Xia is the owner of Recon Group, a holding company that has the controlling interest in five publicly listed companies on the Hong Kong and Chinese stock exchanges, employing 35,000 people in 75 countries.
“If you look at Tony Xia’s business career in China he has been instrumental in the building and regeneration of over 60 new cities,” Hollis told BBC Radio 5 live.
“Through that he shared with us his ambition in global football, his ambition for Aston Villa and for the Aston area as a part of the city of Birmingham, and it is inspirational.
“If he can deliver what he shared with us, it is going to be a great journey over the next few years.”