Costa, Chelsea's top scorer with 15 goals this term, was last month linked with a mega-money move to the Chinese Super League.
Speculation soon subsided and more recent reports have suggested Costa is nearing an extension to his Chelsea contract, which has two years to run come the summer.
Blues boss Conte insisted he was not aware of a new deal being on offer to Costa and vowed to resolve any issues once the campaign is finished.
"I don't know about this situation," said Conte, speaking ahead of Saturday's FA Cup fifth-round tie at Wolves.
"I think now it's very important to be focused on the present and not to look so far forward.
"At the end of the season we will see the situation."
He was then asked if he was confident over whether the 28-year-old Spain striker would be staying.
Conte said: "Yes, I'm confident
I repeat: now it's important to keep the great concentration for the present.
"The present is tomorrow's game against Wolverhampton
We must go in the next round."
One striker who is nearing a Chelsea exit is Dominic Solanke
The 19-year-old has reportedly demanded Â£50,000-a-week in wages
"I think this is his will (to leave)," Conte added.
"I have spoken with him to try to understand his will
But we must have great respect for every decision that the player can take.
"His contract expires in June and he has the full will to stay in Chelsea or to go away."
The Premier League leaders by eight points are seeking to reach the FA Cup quarter-final for the 11th time in 16 seasons.
Chelsea have won the FA Cup four times since 2005-06 and Carlo Ancelotti led the Blues to a league and cup double in 2010.
The double is a target for Conte, who says it should be his players' goal too.
"Usually I like to win and I like to try to win with my team, every competition in every season," he added.
"We must have this winning mentality
When you are Chelsea's coach or you are a Chelsea player, you must have this ambition to try to win every competition that you play.
"For sure it won't be easy
In the league there are six teams very strong to fight until the end to win the title.
"In the FA Cup there are 16 teams
Our target now is to go into the next round.
"Tomorrow the game won't be easy
Don't forget Wolverhampton won against Liverpool away, won against Stoke away.
"We must pay great attention, because this team showed in the recent past that they have the possibility to beat great teams.
"I hope tomorrow the result will be different and Chelsea to go in the next round."
David Luiz will be rested after playing while managing a knee injury sustained in December in a tackle which saw Sergio Aguero sent off for Manchester City
John Terry could take his place in the centre of defence.
"We have the opportunity to give him a week to recover very well and to prepare for the next game," Conte said.
"His knee is okay
(It has) improved a lot."
Marcos Alonso will also be rested and his place at left wing-back could go to Nathan Ake or Kenedy.
But with no midweek game next week, Conte is unlikely to make wholesale changes, so the likes of Costa and Eden Hazard could feature at Molineux.
"All the players are in good form and I have only the problem to make the best choices for the game," Conte added.
Source : PA