Kovac has been linked with a move to Olympiacos, but for now, the Czech midfielder is fully focused on getting off to a flying start with the Hammers.
"The new manager has been good with us and we all want to do our best for the club," he said on the club's website.
"We have some new players like Thomas [Hitzlsperger] and we will see where we are with the Premier League. It is important to start well.
"I am happy to be back with everyone again. It was very good to have the time off, we needed it after a tough season but I want to get going again."