Assombalonga, on loan from Watford, bagged a brace in Saturday's 3-1 win over Dagenham & Redbridge to take his tally to four goals in six appearances.
The forward, 19, arrived on a month-long deal last month but as that arrangement prepares to expire this weekend, he is open to continuing his development at Roots Hall.
"I don't mind staying," Assombalonga told the club's official website. "I am a Southend player at the moment and I'll speak to the gaffer about what happens next.
"I want to play football, score goals and get 90 minutes under my belt each week so this is a good place to do that."
Speaking after his double downed Dagenham, Assombalonga added: "I could have scored four of five goals as the chances kept on coming but I didn't take them. I've never scored a hat-trick as I keep getting braces. I was hoping it would be the day I got my first one but it wasn't to be."