A delegation from the Scottish champions, including Deila, are understood to have held talks with Boyata and the English club earlier this week.
The 24-year-old would be a replacement for his compatriot Jason Denayer, who will return to Manchester City this summer after his successful season-long loan at Celtic.
“We will see what happens,” said Deila after his team’s 0-0 draw against St Johnstone at McDiarmid Park.
“We are looking at a lot of players to try and strengthen our squad and he (Boyata) is one of them. We will see if we can make it happen or not.
“I try to keep the conversations between us to myself. But we are trying to get quality players in to strengthen the team for next season.”
Boyata has been at Manchester City since joining as a teenager from FC Brussels in 2007. He was a key member of the side which won the FA Youth Cup the following year and made his first-team debut in an FA Cup tie against Middlesbrough in 2010.
He made his senior international debut the same year, winning his as yet only cap for Belgium in a Euro 2012 qualifier against Austria.
But Boyata has struggled to build on that promising start to his career and has twice been loaned out by City – to Bolton Wanderers on a season-long loan in 2011, then to Twente Enschede in Holland the following year.
Deila last night admitted Celtic were fortunate to escape with a point from Perth in a match in which St Johnstone were in the ascendancy for long periods.
“It was a miracle it was 0-0,” said Deila. “It was way too open for my taste and we were all over the place defensively.”
James Forrest could have snatched a late winner for Celtic but missed a glaring close-range chance in front of an open goal.
“You saw the ball take a huge bounce up before he hit it,” said Deila. “What can you do? You could grow potatoes on that pitch.”
St Johnstone manager Tommy Wright was full of praise for his players as they edged one point ahead of Dundee United in the battle for fourth place in the SPFL Premiership and a possible Europa League spot next season.
Despite his team missing numerous good chances to win the match, Wright preferred to concentrate on the manner of their display.
“We had 23 attempts at goal against the best team in the country. We dominated long parts of the game,” said Wright.
“I’m delighted with the contribution of every player and it shows people what a good side we are.
“We can play good football, which is often overlooked. I’m very happy with the point and with our performance.
“I don’t think it was down to poor finishing from us. It was down to good goalkeeping, some great defending at times and also a little bit of bad luck when we hit the post twice.
“I feel at this stage of the season it is a good point for us. We know Dundee United will beat us to fourth place if they win their two remaining games, but they are tough games at Inverness and against Dundee that they have to win.”