The Celtic boss has been discussing the 28-year-old's broken finger.
The 28-year-old is currently one of several injury concerns for the Bhoys, having recently suffered a broken finger.
Deila has confirmed, however, that the Celtic star will not need an operation on the problem but feels it may be too risky to play him in this Sunday afternoon's Scottish Cup quarter-final against Dundee United.
"Emilio doesn't need an operation but it might be a bit of a risk to play him," the Celtic boss told reporters.
The Hoops face United in the first round of their double header against Jackie McNamara's side on Sunday, with Celtic then battling it out with Dundee United seven days later - in the Scottish League Cup final.
Among the other injury concerns for the Bhoys are the likes of Charlie Mulgrew and John Guidetti, whom Deila delivered mixed news on during his press conference.
The Norwegian still has a wide range of options to choose from, though, as Celtic's bid to secure a historic treble continues this weekend.
Deila's men will be looking to bounce back from their midweek defeat to St Johnstone, which denied them the opportunity to move nine points clear of second-placed Aberdeen in the Scottish Premiership.