With Sheffield United chasing promotion to the Premier League - they are third in the Championship following Saturday's defeat by Swansea CityÂ - there had been suggestions coaching staff would summon all of their on-loan players back to South Yorkshire for the remaining 18 matches of the campaign.
Slater's situation came under scrutiny when Wilder recently outlined plans to strike agreements with a number of neighbouring clubs aimed at accelerating the development of United's younger professionals. With his friend John Sheridan leaving Brunton Park to take charge at the Proact Stadium earlier this month, there had been speculation he could also leave Cumbria and rejoin the former Republic of Ireland international in north Derbyshire.
But Wilder, the United manager, appeared to allay Carlisle's fears, saying: "All of those agreements, with the lads on loan, there's a date in every contract where they can change through mutual agreement between the clubs and the player.Â
"Will they push to get in at this point in time? No. Are they better playing football? Yes. If I thought it was right to recall them, I would have done. I don't see us recalling any of them."
Slater is regarded as one of the most promising youngsters to graduate from the Steelphalt Academy in recent years, with a number of rival Championship clubs known to be monitoring his progress before United awarded him a new contract. However, with new Carlisle manager Steven Pressley revealing he could recruit five players before the transfer deadline, the 51-year-old and his staff will not want Slater's game-time to be restricted.
Addressing claims that the flow of talent from youth to first team level has slowed at Bramall Lane of late, Wilder used the sale of Harvey Gilmour to Tranmere Rovers to illustrate why some of Slater's contemporaries have been allowed to move on.
"Harvey has done great," he continued. "There might be more deals like that.Â
"It's not just about players for our first team, it's about producing players and having an interest in them.Â
"We have to be fair to people like Harvey too. Are they better playing proper football or under-23's football for the rest of their lives?Â
"For me, that's why you see so many academy players now ending up in Sunday League or local league football. These lads might also come back."
Wilder's words suggest United will look to insert a buy-back option, as well as a sell-on clause, into any future agreements they strike with clubs looking to sign players on the periphery of his squad, although the likes of Nathan Thomas, Ben Heneghan, Samir Carruthers and Ricky Holmes are expected to be exemptions should they eventually depart on a permanent basis.
Speaking before United's visit to the Liberty Stadium, Queen of the South manager Gary Naysmith revealed he hopes to work more closely with Wilder following Callum Semple's successful loan at Palmerston Park.
Although the likes of Chesterfield and Doncaster Rovers are viewed as more desirable destinations by United, because of their proximity to Bramall Lane, Wilder suggested he will accept Naysmith's invitation.
"We've talked about working with the local clubs, even below the league and the National League," he said. "We have relationships with the local clubs and also futher afield; Carlisle with Regan, Harvey with Tranmere and obviously Scotland as well. We don't just send players anywhere."