The 30-year-old dislocated his shoulder in a league encounter between the Potters and Southampton on March 4.
Diouf landed poorly after contesting for an aerial ball at St. Mary’s Stadium and, subsequently, missed his side’s 2-0 defeat to Manchester City on Monday night.
Ahead of the fixture against the Toffees, Lambert stated that the attacker who has notched five goals in 28 league matches this season has stepped up recovery and could be in line for a return to action.
“With regards to Mame, he has a slight chance, but we are going to have to have a look at him over the next day or so,” Lambert told club website.
“There are a few decisions to be made before kick-off and there are a few areas of the pitch that we may need to shake things up in a little bit.”
On Ramadan Sobhi who left a good impression following his introduction as an 88th-minute substitute against Pep Guardiola’s team – his third league appearance this year - Lambert hinted on the winger's chances of getting more playing time on Saturday.
“I thought Ramadan did well on Monday, and he is ready to play,” he added.
“He is enthusiastic and has really good attributes - he has good speed and he has a lot to learn, so he is really in my thinking for the game.”