The former Bayern Munich and Werder Bremen striker is currently back at his former club on loan having been deemed surplus to requirements at Stamford Bridge under Scolari, and has netted 10 league goals this season, adding to the 29 he bagged from 56 Bundesliga appearances in his first spell at the club from 1999-2001.
After netting a further 71 league goals for Bayern, he was snapped up by Jose Mourinho in summer 2007 on a free transfer.
But despite scoring on his league debut in 3-2 victory against Birmingham City, he went on to net just one other Premier League goal - also against Birmingham at St. Andrews - all season, starting just four league games.
Pizarro's return to Bremen has so far proved a successful one. However, with Scolari sacked and Russia national coach Guus Hiddink installed until the end of the season, the German outfit - currently 10th in the Bundesliga - are concerned the Dutchman, or whoever Chelsea's manager at the start of next season is, will want the Peruvian back in London.
"The decision will take time and they will be waiting to see what happens. Who will they buy, who will be moved on," Werder Bremen's general manager Klaus Allofs told Bild.
"We have to be prepared to wait on a decision for quite some time. Potentially up until late August. But we have an agreement with Claudio. He wants to stay with us as he feels happy at our club. That is certainly increasing our chances at this end."
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