Terry scored his fifth Premier League goal of the season and 39th in all - surpassing David Unsworth's record for a defender - in Sunday's 1-1 draw with Liverpool, which all but ended the Reds' hopes of Champions League qualification.
The 34-year-old Blues skipper has equalled his best goals haul for a season of eight and wants to play at West Brom on May 18 and at home to Sunderland on May 24 in a bid for his ninth.
"Looking for one more to beat (my best)," Terry told Chelsea TV.
"Two games to go
I'm fit
Hopefully I play in both
I'll be begging the manager to let me play.
"Two games we need to keep winning and keep pushing on."
Mourinho's management has been lauded by Terry's fellow defender Branislav Ivanovic, who expressed incredulity that the Portuguese had not won a Manager of the Month award this term while tipping the Blues boss for the Manager of the Season prize.
"There is not even a question over who the best manager is this season," Ivanovic said.
"I don't how that (not winning manager of month) happened
But it doesn't matter
If he won one or not, for sure he is the best manager this season.
"He always makes the difference
Most of the games, when you study them, every single one he was important in making sure we won them.
"He has crucial things to say and crucial things to decide
When there is a big game he is always so motivated, but small games too
Inside the team, it's all about him.
"We are all so happy and appreciate the fact we get to work with a manager like him.
"He's developed our squad and changed the mentality
He has done a lot of things for two years and this year really is the best."
Mourinho plans to integrate Chelsea's emerging talent into his side at West Brom, with the final day clash at home to Sunderland one for the regulars on the day the trophy is lifted.
Ruben Loftus-Cheek, the 19-year-old midfielder, made his first start against Liverpool, but Ivanovic believes there are a number of young players who could make the grade at Chelsea, if Mourinho can successfully integrate them into a trophy-challenging side.
"I hope this is just the beginning of a big career," said Ivanovic of Loftus-Cheek, while also referring to Dominic Solanke, Izzy Brown, Andreas Christensen and Nathan Ake.
"We have a great generation of young players
It's not just Ruben.
"We have a minimum of five, six players who can be in our squad and it is great for the manager to give them a chance to play.
"This is the period, the next one or two years, where they need to prove they are really good."
Like Chelsea, Liverpool are looking to the future and life after talisman Steven Gerrard, who is leaving for Major League Soccer's Los Angeles Galaxy this summer.
Adam Lallana believes a collective improvement is the only way to fill the void created by Gerrard's imminent departure.
"He is irreplaceable," Lallana told Liverpool TV.
"I don't think the Premier League or Liverpool realise what we're going to miss out on next season.
"The best way to replace him is not just one individual, it's going to be a combination of every single player."
Not even Gerrard, whose feats have delivered success time and again for Liverpool, can secure Champions League football next term now.
The Reds trail fourth-placed Manchester United by six points - and have an inferior goal difference - with two games to go.
Lallana remains bullish.
"I just feel with the disappointments we've had this season we can really learn from it and push on as a young squad and come back next season and fight for the title and to get into the Champions League places," Lallana added.
Source : PA
Source: PA