Lampard lost his job on Tuesday morning after a dismal run of Premier League results. He has since been replaced by Thomas Tuchel.
The Daily Mail says Lampard is likely to take a mini-break before considering his next managerial position, but remains determined to prove his worth as a top boss.
Despite being ruthlessly dismissed on Monday, Lampard has enhanced his reputation during his time at Stamford Bridge and will be an attractive proposition for rival clubs.
He was 18 months into the job, having taken Derby County to the promotion playoffs the previous season.