While the England international was expected to leave the West London outfit at the end of the season, reports have emerged over the last week revealing that a fresh one-year contract will be placed on the table.
The 34-year-old had been linked with a switch to MLS side Los Angeles Galaxy, but it appears that the midfielder wants to remain with the Premier League outfit.
"Frank still expects to be at the club next season," a source told The Express. "He's keen to get it sorted out as quickly as possible."
Lampard could be reunited with manager Jose Mourinho, who has been heavily tipped to return to the Blues in the summer from Real Madrid.