The vastly-respected Argentine, a hero figure among Leeds followers, was out of contract following the club's return to the top-flight after a 16-year absence, but has been in talks regarding fresh terms.
Some reports have suggested that the 65-year-old has agreed to stay at the club next season.
Speaking on Sky Sports News, Kinnear - who also confirmed that the club's bid to sign former loanee Ben White on a permanent basis has become a 'challenging' one - said: "He (Bielsa) is very, very close. The challenge with Marcelo as we had last season is that he is totally fixated on the preparations for the season ahead.
"He is on the training ground every day and working with the team and doing his analytics and I just need to find the appropriate window to get the paper in front of him for him to sign it.
"But we don't forsee any challenges."
On the club's pursuit of Brighton defender White, subject of several bids from Leeds, Kinnear added: "Ben had a wonderful season for us and is a player we rate very highly and know the fans love.
"We think Ben enjoyed his time here and have made no secret of the fact that we'd like to bring him here permanently. We also have to be very respectful of the fact he is a Brighton player and is training with them currently.
"There have been discussions and I think it is going to be challenging to make him a Leeds United player. But if it is not Ben White, we have other options that are in advanced stages and we will be closing in on one of them soon."
Leeds are scheduled to start the 2020-21 season with a glamour trip to face champions Liverpool at Anfield on September 12 and also host Manchester City early in the season at Elland Road on October 3.
A glamour April sees United host Liverpool, Manchester United and derby rivals Sheffield United at Elland Road, with the tantalising potential of fans being back at the ground.
On the club's opener, Kinnear said: "There were a few wry smiles, but we have worked so hard to be playing in arenas like that against teams like that. We just want to bring it on."
On some marquee home games in April, he added: "We would love crowds to be back by that stage. We are very pleased to be here, the boys are at the training ground now and looking at the fixtures and are excited and up for the challenge and we are not daunted."