The 70-year-old took over at St Andrew's last month to save the club from relegation in the Championship following a dramatic slide down the table after the sacking of Gary Rowett.
Redknapp achieved his goal with victory on the final day of the season and met with the club's owners on Sunday to discuss the possibility of extending his stay.
"I've had a chat with the owners, I met them last night for the first time. I had a really interesting meeting. They were very nice, very good people and they obviously want to take the club forward. They're not going to throw crazy money at it to try and achieve that, but they will invest. It's just a case of wait and see. I'm going to have another couple of meetings with them and we'll see where we're going," he told BBC WM
"I would think within the week [a decision will be reached]. I'm not playing hardball with anybody. It's just a case of making sure. It's a big ask for me again. I've come out of it, life is quite good for me at the moment, I've had no pressure and am quite enjoying doing what I'm doing every day when I get up.
"I've been managing an awful long time so to go back into it again full time is a big, big decision for me. I've got to make sure I do what is best for myself as well. I'm interested in staying but there's a lot of work to be done, it's a tough division. Look where teams like Norwich and Villa, who spent absolute fortunes, have finished this year. But I've been really impressed with the club and the people at Birmingham."
Redknapp won two of his three matches in charge of Birmingham to guide them to safety.