Dirk Kuyt became the first-high profile departure from Liverpool after the Dutch striker signed a three-year contract with Fenerbahce.
The Turkish giants paid a mere $1.5 million for Kuyt, who is believed to earn $3.3 million per season.
The 31-year-old, who had one year on his contract remaining, had hinted his six-year spell at Anfield could be over after finding playing time hard to come in a difficult campaign last season. Kuyt was bought by Liverpool for $14 million from Feyenoord in 2006 after a prolific spell with his hometown club.
The Dutchman, however, found goals hard to come by in the English Premier League and was shifted to the right of midfield where he excelled with his tireless work rate.
"After six years I am ready for a new challenge. This is a fantastic club to continue my career," Kuyt told Sport-Promotion's website.
"(The club and supporters) I will always carry in my heart.
Kuyt insisted Rodgers' appointment had nothing to do with his decision. "The appointment of the new coach has nothing to do with it. When Fenerbahce came to me and made their ambitions known, from the first moment I was sold. They give me the confidence that I lost."
Rodgers hinted Liverpool might replace Kuyt by going for Gylfi Sigurdsson. Swansea agreed a $10.5 million fee with Hoffenheim for the striker, but Sigurdsson is yet to sign a contract with the Welsh club. Rodgers pushed the Swansea management to sign the Icelandic player, but with the manager now moving to Liverpool, things have changed.
"Gylfi came to Swansea because I was there as manager and his scoring record was fantastic," he told the British media.
"I pushed the club to make an agreement and they did that in terms of the fee, and agreed the salary. So I have said to (Swansea chairman) Huw (Jenkins): 'I'm not going to do anything untoward. This is a guy you want, but it is down to Gylfi'.
"If he comes on the market, I have to be interested. He knows that I rate his qualities and abilities.
"I said to Huw: 'If I speak to the kid I'll tell him to speak to the new manager, whoever that is'. But if he's not comfortable with that, he's in the market place then, and I have to look at him."
Another Liverpool forward that could be on his way from Anfield is Luis Suarez. The Uruguayan's national team-mate Martin Caceres told Tuttosport, Suarez might be tempted to move to Caceres' club Juventus. "It is true that Luis and I have talked about Juventus. He asked me about the club without going into any details.
"I told him that Juventus are a team that always want to win. He liked what I told him about the club, but he's happy at Liverpool at the moment."
Rodgers is also keeping an eye on Tottenham Hotspur's Giovanni Dos Santos, according to ESPN Deportes. The Northern Irishman was considering a move for the former Barcelona midfielder when Rodgers was with Swansea and could now look to bring him to Anfield.
Meanwhile, Craig Bellamy has confirmed he will be a part of Great Britain's Olympic squad. "I am in the Olympic squad, but I was supposed to keep it quiet," Bellamy was quoted as saying in The Sun.
"It's a different challenge, but the Olympics is a one-off."