Seven straight wins have lifted the Warriors into third place in the table.
"We've put ourselves in a good position and the players are confident they can finish off well over the next three games," Murray told BBC Scotland.
"There is a great desire and passion among the guys to do well again this year. I'm confident that we can do it and go to another Pro12 final."
Glasgow lost in the semi-finals in 2013 before reaching the final 12 months later, and went one better last year by beating Munster in the final to be crowned champions.
The Warriors are two points behind leaders Leinster and Connacht with three games remaining - away to Scarlets, home to Zebre, and away to Connacht in the final round on 7 May.
The top four enter the end-of-season play-off semi-finals, with the top two enjoying home advantage.
"We've managed to steadily climb our way back up the league and we've got ourselves back into the top four," said Murray.
"Our target is to get in the top four and then, from our performances, we might get in the top two.
"But we are in a good place and we're starting to play some really good rugby at the right time of the season."
Glasgow travel to Wales to face a Scarlets side sitting three points behind them in fourth and who will be looking to leapfrog their visitors with a victory.
"We've played them there already this season in Europe and we beat them 9-6, so we'll take a lot of confidence from that," said Murray.
"Our target is to win all three of those games and it depends on what happens in other games.
"Other teams in the top four all have hard games, so there could be a lot more ups and downs for all the teams.
"There are four good sides in the top four at the moment and, for us to put ourselves in a position where we win it, we have to be better than them."
Murray thinks the prospect of a final in Scotland, on Saturday, 28 May, should also provide motivation.
"What a great opportunity to go play at a Pro12 final at Murrayfield, but there's a lot of rugby to be played before then," he added.

Maya Kantengule was found at the bottom of a swimming pool at Waveney River Centre holiday park in Burgh St Peter, Norfolk, on May 1 2016.
She was declared dead later that day at James Paget University Hospital.
South Norfolk Council environmental health officer Chris Coker said people swam at the centre at their own risk.
Maya's father, Livial Kantengule, said in a written statement at the inquest in Norwich that he spoke to Jane Rainer, the mother of his daughter's best friend, as he arrived and decided not to wait at the pool during the party.
He returned there with his wife, Glenda, after receiving a message there had been an accident.
Maya had already been taken to the hospital near Great Yarmouth. Her parents were at her bedside when she was pronounced dead.
Mr Kantengule said he did not ask if there was a lifeguard.
"Jane used to volunteer to help with the swimming lessons, so we assumed Maya would be adequately supervised while in the pool," he said.
Maya, from Smith's Walk, Oulton Broad, near Lowestoft, Suffolk, attended Dell Primary School.
Jaqueline Bell, a teaching assistant at the school, said in a written statement that Maya started weekly swimming lessons in reception year.
"She was nervous in the water and would use armbands and a woggle," she said.
Mr Coker told the inquest the indoor pool at Waveney River Centre could be privately hired.
He said it was 1.5m (5ft) at its deepest and signs were up stating there were no lifeguards on duty and that people swam at their own risk.
The inquest, expected to last two days, continues.
Assistant coach Kenny Murray says there is a growing belief at Glasgow Warriors that they can retain the Pro12 title.
[NEXT_CONCEPT]
A seven-year-old girl drowned at her best friend's birthday pool party while there was no lifeguard on duty, an inquest heard.