The three-Test series begins with a day-night match - the first in England - at Edgbaston on Thursday.
The tourists have lost six consecutive Test series, their most recent win coming against Bangladesh in 2014.
"I am concerned with the way we are playing," said 53-year-old Ambrose, who played 98 Tests for West Indies.
Speaking on BBC Radio 5 live's Tuffers and Vaughan Cricket Show, he added: "I am hoping they can at least win one Test or compete, but, as a realist, I am not too sure they will."
West Indies will be without several key players - including Chris Gayle, Darren Bravo, Darren Sammy and Marlon Samuels - after a number of disputes in the Caribbean between the board and its players.
Ambrose said the inexperience in the squad is a "serious problem".
"I still believe if we had all those names, our cricket would be better," he said of the side who are eighth in the Test rankings, above only Bangladesh and Zimbabwe.
Many of West Indies' star names opt to play in lucrative global Twenty20 competitions rather than in the domestic league.
"Look at the Twenty20 squad. We have them players available and they have always been a force," said Ambrose, who took 405 Test wickets.
"According to the Cricket West Indies board, you have to be available to play all the first-class games in the region to be eligible for the Test team.
"I don't have a problem with that, but Cricket West Indies need to be more lenient with their players if they want their best team.
"So many players are starting their careers so have no-one to turn to who is a senior pro."
Ambrose will be a part of the Test Match Special commentary team for the England and West Indies series this summer.
West Indies will have to "play exceptionally well to even compete against England", says legendary fast bowler Curtly Ambrose.