Panathinaikos have completed the signing of Marcus Berg and the striker could reportedly be followed out of Hamburg by Michael Mancienne, Slobodan Rajkovic and Paul Scharner.
Berg has signed a four-year contract with Panathinaikos and has cost an undisclosed fee after becoming the Greek club's third summer signing.
The Sweden international joined Hamburg in 2009 from Groningen, but he struggled to make a lasting impact after scoring five goals in 43 appearances.
Hamburg are now likely to offload further players after general manager Oliver Kreuzer confirmed the priority is to bring in a new striker.
"We are in no hurry and we are not feeling any big pressure, but we are out to sign a new striker," Kreuzer told BILD. "Therefore, it is necessary to keep on selling.
"The most important thing in this matter is that those players are leaving our club."
Reports suggest that former Chelsea duo Mancienne and Rajkovic will be allowed to move on, despite having two years left on their contracts.
The versatile Scharner spent the second half of last season on loan at former club Wigan and the Austrian has a further year to run on his Hamburg deal.
City are beginning a new era under Pellegrini following the sacking of Roberto Mancini in May.
Pellegrini has now met most of his squad for the start of a pre-season programme which includes trips to South Africa, Hong Kong, Germany and Finland.
Kompany told the club's website: "I think all of us have done some preparation work during the holidays because the guys look very sharp after a long break, so that's great.
"It was also nice to start work with the new manager and I think his approach with the team today was really good.
"It's important now to try and improve on the last campaign and make sure that whatever the new manager brings in, that we try and make it our own as quick as possible."
City lost their Premier League crown last season and were surprisingly beaten by Wigan in the FA Cup final, events which preceded Mancini's departure.
But since then there has been change with, as well as Pellegrini's arrival, the club signing two high-profile players in Fernandinho and Jesus Navas. Carlos Tevez has also left for Juventus.
Kompany said: "We're at a big club, so the only goal we can have is to win trophies.
"There's about six or seven clubs in England alone in this situation, so it will be very competitive.
"Our objective this year is to win things and to play well together. We all know that we have to be very strong as a team and bond with each other."
