Steve Evans believes Leeds United will reach agreements to extend the contracts of Lewis Cook, Charlie Taylor and Alex Mowatt before the start of next season – on the strength of the squad he plans to put together this summer.

Evans, who revealed on Friday that he expects to sign a deal to stay on as head coach for the 2016-17 campaign once Leeds are safe from relegation, said talks were ongoing with the agents of Cook, Taylor and Mowatt with all three academy products running close to the end of their existing contracts.

The trio are tied down until June 2017, leaving United under pressure to negotiate improved terms and avoid a repeat of the situation which saw Sam Byram – another player produced by Leeds’ academy at Thorp Arch – leave for West Ham United in a £3.7m deal last month.

Byram quit Leeds after months of speculation about his future, caused by Leeds’ failure to agree a new deal with him and an initial offer from owner Massimo Cellino which asked the right-back to take a wage cut. He was sold with only six months left on his contract.

Byram’s exit was the latest in a line of unwelcome departures from Elland Road, before and since Cellino’s takeover in April 2104, but Evans insisted he was not fearful of losing Cook, Taylor or Mowatt – and claimed Byram’s decision to move on had been influenced by Leeds’ inability to challenge for promotion from the Championship.

Uwe Rosler, the head coach who led Leeds into this season, was sacked in October after only 12 games in charge, making way for Evans to replace him. United have not held a place in the league’s top six at any stage since the campaign began.

“I think Sam last summer – and I’m only guessing – didn’t think there was a squad here that would challenge for the Premier League,” Evans said. “That’s probably what he was looking at.

“He had a desire to play in the Premier League. If I was the father of the Cooks, the Taylors, the Mowatts then you want them to play in the Premier League, don’t you?

“But I’d also want them to play there for Leeds United – so I’d have a look and see if they’ve really got a squad which is challenging.

“Do I think Sam would have left if Uwe Rosler was coach and Leeds United were sitting in the top six? He’d still be a Leeds United player. It’s great to see him do well at West Ham but I think he’d still have been at Elland Road.”

Cook, the 19-year-old prospect who has been capped by England at youth level and claimed his first league goal with a spectacular strike in Tuesday’s 1-1 draw with Fulham, signed a new deal as recently as last May.

Leeds handed him a two-year contract as his previous deal prepared to enter its last 12 months. Taylor received a three-year deal in 2014 while Mowatt – the club’s reigning player of the year – was tied down to 2017 during the 2013-14 term.

Evans said: “I don’t know if the status would be advanced but I certainly know the president and Paul Bell (United’s executive director) have been speaking to representatives of those guys. That will go where it goes.

“There’s no pressure from me, the club decide what’s right and what’s not right, but I think we won’t be going into next season with them only have one season left on their deals.”

United are in the bottom half of the Championship but far removed from the relegation zone and Evans said he had been told by Cellino that he would be confirmed as head coach for next season as soon as Leeds were unequivocally safe.

Leeds travel to Brighton tonight, the first of 14 remaining league fixtures, looking to improve a run of one win in 10 matches.

Cook’s long-range shot on Tuesday lit up a tense meeting with Fulham and Evans admitted the young midfielder – targeted by Premier League club Bournemouth in January – would send his value soaring and attract increased interest with a run of goals.

“If he keeps playing as he is then of course we’ll get tested (by bids),” Evans said. “But there was a massive test with Cook in January. It wasn’t just Bournemouth. There were four or five more clubs who expressed a real interest, to the point where I thought the offers would have been acceptable. The president’s view was that he’ll get better.

“I think everyone accepts that if Lewis adds goals to his game, he probably becomes unbuyable for (some) clubs in the Premier League.”