City stretched their unbeaten run at St Andrew's to 13 games in the league with Sunday's 1-1 draw with Liverpool.
If Birmingham can now avoid defeat in their final two home matches with struggling Hull and Burnley, it will beat their previous record of 14 set in 1974.
"We've got two games left, so why not?" said Jerome on the prospect of ending the season on a high.
"We will be playing two teams who are struggling near the bottom of the table, but we can't take that for granted.
"We've got to keep doing what we've been doing and what has got us good results and good points against the bigger teams.
"If we take performances like we produced against Liverpool into those two games then I am sure we will come out of the rest of the season unbeaten at home and it would be a great achievement for us.
"We want to finish on a high note and then come back refreshed for next season, ready to go again."
Striker Jerome believes the reason behind their phenomenal home run comes down to the mentality of the players feeling no game is ever a lost cause.
"There is a belief now we can come back in a game if we go behind," Jerome told the Birmingham Evening Mail.
"We have shown some great spirit and some great character. It takes a lot to do that.
"Dropping your head is easily done, especially against a side like Liverpool, and letting them get a second goal.
"But like we have done a lot this season, we came straight back at them and started to play a little more football when we went 1-0 down.
"It is like we were waiting for that kick up the backside to get us going."