The executive council of the ASTI is to consider pay proposals this weekend in a bid to resolve their ongoing dispute.
Details of the deal emerged today, including an opt-out clause for members who do not want to carry out supervision and substitution duties.
There is also a proposal to gradually increase pay for newly qualified staff to almost €34,000 a year.
The deal is believed to be similar to the ones agreed with the other teachers' unions. The TUI and INTO unions have already signed up to the Lansdowne Road Agreement.
The ASTI's standing committee discussed the proposals this evening but did not come to any decision.
In a statement, the ASTI said: "At its meeting today the ASTI’s 23-member Standing Committee considered documents issued by Anna Perry, Chair of the Teachers’ Conciliation Council, following talks aimed at resolving current disputes between the ASTI and the Department of Education and Skills.
"Standing Committee made no decisions regarding the proposals. ASTI Central Executive Council will meet on Saturday, December 3rd," it adds.