The players have denied the allegations, and at least one has offered to take a lie detector test to prove his innocence.
Israel suffered an 8-0 aggregate defeat at the hands of Denmark but the tie was effectively over after Israel lost 5-0 last weekend at home.
But the failure on the pitch has paled into insignificance with reports that Israeli players partied with prostitutes before and after the drubbing.
The Ma'ariv, a leading Israeli daily newspaper, quoting unnamed sources, including members of the national team said prostitutes were called to the team's hotel in Tel Aviv.
National coach Shlomo Scharf said he was looking into the reports but said it was possible that hotel staff quoted in the paper had actually seen players' wives and girlfriends.
The two-legged tie was billed as Israel's most important ever and victory would have seen them qualify for the European Championships for the first time.
BBC Middle East correspondent Paul Adams said the country was looking for reasons for the defeat and sex has become the prime suspect.
Doctors and politicians have taken to the airwaves to discuss whether late-night frolics sapped the strength of the Israeli players.
Israeli Internal Security Minister Shlomo Ben-Ami is quoted as saying the Danish team was so much better than Israel that "if it had been the Danish players who partied with call girls", the result would have been the same