The Toffees are reported front-runners to bring the Croatian from Glasgow, but their Scottish boss remained tight-lipped over a possible move for the 26-year-old
The Croatia international has been the subject of intense speculation after scoring 17 times in 28 appearances this season and the Glasgow club have already rejected a bid from West Ham for the forward.
Reports suggest that the Toffees could now be leading the race to land his signature, but Moyes refused to comment on these claims and underlined his unwillingness to discuss potential signings to the detriment of his squad.
"I never talk about players at other clubs, I wouldn't do that," he told reporters.
"I don't like it and I didn't like it when I was a player and I kept hearing there were other centre-halves coming in to take my position. I wouldn't talk about players at other clubs.
"If there was any news I would give it to you. You will need to wait until midnight [Tuesday] and then we will let you know what is happening."
Despite his refusal to discuss Jelavic, the 48-year-old admitted he is looking to bring in players following the departure of Diniyar Bilyaletdinov to Spartak Moscow.
He added: "I said probably a month ago that I would hope to bring two or three players in during the window, so that answer to that is yes."