The 25-year-old scored all three goals as Hannover defeated Werder Bremen in the Bundesliga on Sunday, taking his tally of goals for the current campaign to six in just five appearances.
That strike rate has the Lower Saxony club worried about receiving offers for the forward, which is why they may renegotiate his terms.
"That has got to be our aim," said Hannover's chairman Martin Kind after Sunday's match.
"Maybe the break for international matches is just the right time for us to draw up a schedule, but we are not under any pressure."
Abdellaoue still has two and a half years to run on his contract with Hannover, but Kind wants to offer him a home for life.
"He is a great lad and a fantastic player," he added.
"He is not for sale. If possible, we would like to tie him down to Hannover in the long term."
However, even Kind knows that the player has a price and his club may struggle to keep hold of him if he carries on scoring at such a rate.
"It will be the market which decides that," he admitted.
"We will not be able to decide it."