Peers are set to vote on a Labour move to overturn the clause when the Local Government Bill reaches report stage on Thursday.
Two previous attempts by Labour to scrap Section 28 have foundered, largely in the face of opposition from the Lords.
However, opponents of the clause calculate that as few as 20 peers changing their position from the last vote on the issue, in 2000, would result in success for them.
If that happens, The TES understands that the Conservatives would find it hard to reinstate the clause before it leaves the Lords. The Commons has already voted to scrap Section 28.
Both Labour and the Conservatives have given their peers a free vote on the issue at report stage. A majority of Tory peers support Section 28, and they were backed in 2000 by a minority of Labour rebels.
The Liberal Democrats will vote to scrap the clause.
Conservative spokeswoman Emily Blatch is gearing up to challenge the Government by tabling an amendment which, she said, would actually strengthen Section 28.
She tabled an amendment, which was not voted on, during the Lords debate last month. This would have provided for parents to be sent copies of any book, video or teaching aid used in sex education.
If the vote goes Baroness Blatch's way, there is some speculation that the Government might not move to overturn it when the Bill comes back to the Commons.