Fulham, who were recently bought by Khan from Mohamed Al-Fayed, finished 12th in the Premier League last year but were only seven points above the relegation places.
The Norway centre-back, also captain of his country, says that whilst extra signings would be a bonus, he is still wary about the possibility of going down.
He told the London Evening Standard: "My concern every year is to get to 40 points and I am hoping that will be as early in the season as possible.
"It might sound like a lack of ambition but I am very happy to stay in the Premier League because I know how tough it is.
"We have a lot to thank Mohamed Fayed for, but the new owner seems like a really good guy and has been successful in what he has done in the past."
Manager Martin Jol had already been active in the transfer market prior to Khan's takeover, signing Maarten Stekelenberg, Sascha Riether, Derek Boateng and Fernando Amorebieta.
Since the American's purchase of the club, Jol has added Adel Taarabt on loan from QPR, and has previously said he still wants to make more acquisitions.
Hangeland, who recently signed a new contract at the club, hopes the additions will give the squad more depth
"We have good competition now and it is hard to pick the best starting line-up because there are so many players on the same level," added the 32-year-old.
"That gives the manager a headache, but a good one."