The 33-year-old Nigerian international, who is out of contract next month, claimed his second winners’ medal as a Rangers player when he helped them keep a clean sheet in their Scottish Cup final win over Hearts at Hampden on Saturday.
“Everyone who watches me move around the club know that I have absolutely fallen in love with this club,” said Balogun.
“What I’ve described about getting knocked down and standing back up, it’s my career.
“I had a lot of downs and I always pick myself back up. That is why probably me and Rangers are quite a good fit.
“Even the Cup final, I thought I had to go through this with all the support that was outstanding, to get that into my DNA even more.
“I would love to stay, I think they know that. I hope I can announce something about my future with Rangers soon.”
Balogun believes Rangers are destined for more success under Giovanni van Bronckhorst’s management after they recovered from Wednesday’s Europa League final penalty shoot-out defeat against Eintracht Frankfurt to overcome Hearts 2-0 after extra-time.
“There are a lot of great things about Rangers right now,” he said. “Looking at the whole season, it wasn’t easy.
“We lost one manager halfway through almost. To regroup with the new manager, it wasn’t easy for them because they have their own style and philosophy.
“But we showed we have great resilience and we can still play very attractive football.
“These wins, the way we compete, even if we lost a few important games, it’s attractive to loads of players especially with the European run.
“It’s going to help the manager massively to have a full pre-season. He had to take over what was there.
“He found a very solid basis but every manager has his own style and it will really help them not just to train like once or twice with the full team between matches.
“I am genuinely excited about what is to come. We’ve made huge steps forward, you could see that in all the big games. You could see a certain dominance and a style of play.
“I think we deserved it today. We said to ourselves, we had to suffer a lot of setbacks these past weeks.
“With the league, then Wednesday. You could feel that a little bit. We had to shake it off in the first half.
“I think we’ve done a tremendous job coming back in the second half the way we did.
“In extra time it wasn’t easy. Most of the boys played 120 minutes, so a huge compliment to the guys.
“It’s massive not to finish the season empty-handed, to get another trophy to our name and to play alongside legends of the club like Steven Davis and Allan McGregor.
“When I look into their faces, you just know what it means and how big this is to win another trophy.”