Wright took charge of the Spireites for their 1-1 at Gillingham after John Sheridan was sacked by chairman Dave Allen.
The former Scotland winger was number two under Sheridan at Oldham and Chesterfield, but says he is now ready for the top job.
Wright told the Derbyshire Times: "John has given me his blessing and being professional you have to deal with these things.
"I have enjoyed it so far and if everything goes well, I hope to be having a talk with (chief executive) Chris Turner and Dave Allen.
"I will give it all I can. I think the players respect me and I think they are behind me."