Liverpool won the game 4-0 but at one point striker Luis Suarez collected some objects as he prepared to take a corner early in the match at Anfield.
It is alleged around a dozen coins were thrown from the Anfield Road End - part of which houses visiting supporters - during the first half.
Another object also appeared to be thrown towards players as Reds captain Steven Gerrard celebrated scoring the first goal at that end.
No players were hit and Liverpool manager Brendan Rodgers said Suarez did not complain about any such issues.
Rodgers said: "He never mentioned nothing, no."
Merseyside Police said in a statement: "Merseyside Police can confirm it is investigating following reports of some missiles being thrown during the Liverpool v Everton football match this evening, Tuesday, 28 January.
"The incidents took place during the first half of the game when a number of coins and other small objects are believed to have been thrown from the stands onto the playing area.
"Officers are requesting CCTV from the stadium and will review any footage as part of inquiries to establish the full circumstances surrounding the incidents."