Ajeti was brought in at West Ham during the summer transfer window, but has only been used sparingly so far.
Pellegrini has opted to keep the Swiss striker in reserve, with his only appearance for West Ham so far coming in cup competition.
Ajeti failed to make much of an impact against Newport County, even though the Hammers won 2-0 on that occasion.
West Ham now face a tie against Oxford United later this evening, when Ajeti could get his second chance.
And the £8 million man (BBC Sport) insists that he is capable of performing a more regular role at the London Stadium.
“I feel in myself that the coach [Pellegrini] trusts a lot in me and I trust him too, and he knows I’ll do everything to get my minutes on the pitch,” Ajeti said.
“The coach knows my qualities and I have big self-confidence and believe I can rise to every challenge.
“It’s just important to continue to do my work as well as I can and hopefully more opportunities will come. I am ready, and the coach knows he can put me in every game.
“I’m waiting for every game, for the cup games and even in the Premier League.”
Ajeti hasn’t really been needed at West Ham yet, as Sebastian Haller has led the line so well.
However, as the demands of the season become harder it will be important that he is fully up to speed.
West Ham go into tonight’s game as heavy favourites, with Oxford currently sat in mid-table in League One.
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