The 25-year-old striker was arrested on suspicion of assault last week, but was in the West Ham team that won 2-0 at Arsenal and the Senegal international is likely to start for the Hammers when they welcome Leicester to Upton Park.
Police held the player last Thursday on suspicion of attacking a girlfriend in east London, The Sun reported, but Bilic said that from a football perspective there is no reason why Sakho will not be in his team.
"Well, he's training," the Croatian replied when asked about the situation.
"He played against Arsenal
He was here every day, he looks okay, he looks happy, he's not worried
For all these things I'm happy.
"For all other the aspects of this problem you should talk to Diafra
Of course I'm concerned, I spoke with him
But he looks very positive, he's not worried about it
Therefore, he trained normally this week
I am happy with him"
While Sakho remains in Bilic's plans at this early stage of the season, one player who will not be involved against the Foxes is midfielder Morgan Amalfitano.
The France international was not in the squad for the victory at the Emirates and was conspicuous by his absence at the club's open training session on Tuesday.
It later emerged he had missed a team meeting and was punished by Bilic, who made him train with the youth team.
Although Bilic says the reports of a bust-up were sensationalised, he did suggest that Amalfitano has no future at West Ham.
"He's not in the first team any more and that is it," he said.
"I have to protect the team
I said it to players at the start, these things are not new
They are more or less the same at every football club.
"My first job is to protect the team, t o keep the team as a unit in the best possible way
And if I feel me and my staff, if I feel that someone is damaging it in a way, I have to react
And I did that
"It was nothing or nowhere near what was in the papers
It was not brawling in front of players
This was just a quiet meeting between the two or us where I explained the situation
I had to do it to keep the harmony, to keep everything in place."
It has been a busy first week of Premier League management for Bilic, who also clarified why West Ham had opted against offering a contract to Joey Barton.
The former QPR captain is a free agent and appeared set to sign for the Hammers, who then pulled the plug on the deal amid widespread criticism of the move from the club's supporters.
Asked if the deal was scuppered by the opposition from a large number of fans, Bilic said: "No, no, it was altogether
Not just one thing.
"We were thinking about Joey and I like him as a player
We discussed, we had some talks and ideas about him
But after that we decided and Joey also not to do it.
"It was not the best timing
Joey is great lad and a good player
He wished us well and we also want to wish him well."
Source : PA
Source: PA