Emenalo retired from the position earlier this week after a run of six years in the job, against the wishes of Roman Abramovich who did not feel a change was needed.
The Blues have now started the process of finding a replacement, with The Express suggesting that Lampard is among those being considered to fill the position on a permanent basis.
Marina Granovskaia will oversee day-to-day running of the club behind the scenes for the foreseeable future, as Chelsea do not want to rush a decision.
Italian football legend Andrea Pirlo has also been touted as a possible option to come on board at Stamford Bridge in some capacity, having announced his retirement from playing earlier this week.