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.
Assistant coach Kenny Murray says there is a growing belief at Glasgow Warriors that they can retain the Pro12 title.