The youngster made his Premier League debut for the club last season.
The 17-year-old has only made five appearances in the Premier League for the Baggies, but did enough to earn their Young Player of the Season award, and has now been rewarded for the bright start to his career by being offered his first professional deal.
And despite the Express and Star reporting that some big clubs have been monitoring his progress, it appears that he is ready to quash any speculation by committing his immediate future to Tony Pulis' side.
The news that Leko is ready to put pen to paper will provide the side with a big lift ahead of the new campaign. Though he did not make a huge number of appearances for the club last term, he was able to display his talent as he contributed an assist during the side's 1-1 draw with Liverpool on the final day of the campaign.
And with Stephane Sessegnon departing, he may find that he receives more chances to impress next season due to the lack of wide options currently within the squad.
The Express and Star adds that he may not be the only youngster to confirm his commitment to the Baggies, with midfielder Sam Field - who also made his debut last season - also set to agree terms.