The Merseyside giants suffered another defeat on Sunday, losing 2-1 at West Ham United to slip to their 17th league loss of the current campaign.
Frank Lampard’s side sit just three points above the bottom three and face second from bottom Burnley away from home on Wednesday evening.
They have a host of tough fixtures between now and the end of the season with games to come against the likes of Manchester United, Liverpool, Chelsea and Arsenal.
And Everton legend Reid admits he is seriously worried about the prospect of relegation from the top flight.
“Yes [I’m concerned Everton could be in the Championship]”, he said on talkSPORT.
“It’s a big game Wednesday and then Manchester United.
“Having looked through the fixtures, Everton have got some real tough games.
“I just hope we get enough points to keep us in the league and then hopefully grow the club, but it’s going to be hard because going to Burnley on Wednesday is going to be a really difficult game.
“Sean Dyche has done a great job with the budget he has every year.
“Everton have just got to get enough points to stay in the league, but am I worried, yes.”
After playing Burnley, Everton then have two games in a row at Goodison Park with Manchester United and Leicester City set to visit.
