Boniface returned from injury on Saturday but was on the bench for Leverkusen's 2-2 draw with RB Leipzig after German media reports linked him with a transfer to Saudi club Al Nassr.
He was then left out of training ahead of Leverkusen's 2-0 Champions League win over Czech side Sparta Prague on Wednesday.
"He will train again tomorrow. I believe he is staying with us," Alonso told reporters after that win.
"So I have to say that I am satisfied, I am happy. He is comfortable here, so I don't believe that this is a big stress for him."
The Nigerian has scored eight goals in 15 games in all competitions. Last season, he netted 14 goals in 23 league appearances to finish as their top scorer and played a pivotal role in securing Leverkusen's first Bundesliga title.
Boniface staying at Leverkusen could open the doors for Aston Villa's Jhon Duran to join Al Nassr instead.
The Colombian forward is also a reported target for the Saudi club, who are looking to bolster a frontline that already features Cristiano Ronaldo and Sadio Mane.