Town currently sit eighth in the table after eight games – the highest they have been since Leahy has been at the club.
It has been a positive start to the season for Shrews after they recorded back-to-back wins away at Forest Green Rovers and against Exeter City at the Meadow.
And Leahy is urging his team to keep pushing themselves ahead of their trip to Port Vale at the weekend, and when the final whistle arrives, he wants to be even higher in the table.
He said: “I want to stay in that top-half, like all of us do.
“So we will be doing our best Saturday to make sure we climb higher than we are now.
“It is still early days in terms of saying play-offs and all that.
“But we just want to be as high as we can, and we do not want to drop from where we are.
“If it doesn’t then we will always push to be higher.
“Come Saturday at five o’clock, I want to be higher than where we are.”
Leahy was made captain before the team’s first game of the season at Morecambe.
And the former Walsall and Bristol Rovers man said he is someone who believes it is ‘important’ to look at the table saying it helps him to strive to be better.
“I look at it from the first game of the season,” he continued.
“It is important to look at the table because you can see where you could reach to and where you could possibly drop to as well.
“We are up there at the minute it is the highest we have been since I have been here.”
It is the highest Town have been in the league since 2019.
The team have had to show real character at times, coming from behind to beat Exeter and Wycombe.
And assistant manager Aaron Wilbraham believes winning games and being near the top of the table gives the players a lift.
“It’s always nice to be at the top end of the table, and when you get there, you want to stay there,” he said when asked about Town’s league position.
“It will give the lads confidence when they see that after they get home.
“We want to win as many games as we can and see where it takes us.”