The Hammers are currently chasing Manchester City in fourth.
The Hammers have enjoyed a fine first campaign under manager Slaven Bilic, with them currently fifth in the Premier League table.
They are just one point behind Manchester City in fourth, and five behind London rivals Arsenal in third, meaning a Champions League place is very much up for grabs.
West Ham's current form suggests they will be fierce challengers as well, and Bonds says he is confident they will make it into the top four by the end of the campaign.
"I genuinely believe we can now finish in the top four,” he told whufc.com.
“We are good enough with this terrific squad and I see no reason not to believe we can't reach the Champions League places.
“You have to congratulate the manager and owners on where they have taken us this season."
If West Ham are to make it into the top four, the form of Dimitri Payet will be key to their hopes.
The Frenchman has enjoyed a fantastic first season in England since his move to Marseille, quickly becoming the star man in this Hammers team.
His form with France over the international break certainly suggests he is not slowing down, and West Ham will be hoping he can continue his impressive displays from here on in.