SDLP North Belfast MLA Alban Maginness and Lagan Valley DUP MLA Paul Givan have jointly tabled the amendment over "grave concerns" about private clinics operating in Northern Ireland.
They want to ensure it is illegal to carry out an abortion, except through the NHS.
The law in Northern Ireland means abortion is already illegal, except in limited circumstances where the mother's life and/or mental well-being are considered to be at significant risk.
But if those conditions are met, there is no set gestation limit - which means that, if approved by a doctor, a pregnancy can be ended at any stage.
In a joint statement, Mr Maginness and Mr Givan pointed to the opening of a Marie Stopes sexual health clinic in Belfast as having presented "a challenge" to legislators.
The clinic offers a range of services including ultrasound scans, STI testing and treatment, HIV testing, short and long-term contraceptive options and emergency contraception.
It also offers medical abortions which must adhere to the law as it stands in Northern Ireland and also be carried out before the ninth week of pregnancy.
According to the MLAs, "grave concerns surfaced regarding the ability of private clinics to carry out abortive procedures without any form of transparency, oversight or accountability to the public".
Everyone's focus must be on promoting better health and empowering women in particular to prevent crisis pregnancies.
Alban Maginness, SDLP & Paul Givan, DUP
Mr Maginness and Mr Givan added: "Furthermore, it is dangerous that any organisation should receive financial reward from carrying out abortions - especially where there are such distinct legal parameters governing the matter.
"A financial reward for carrying out an abortion is incompatible with the spirit of our legal framework, which governs abortions."
The pair say that, within the NHS, "the welfare of both mother and child will be the primary concern rather than profit margins". They also point to "rigorous levels of scrutiny" faced by the NHS.
They are calling on MLAs across all political parties to considering supporting the amendment, which will state that "any person who ends the life of an unborn child at any stage of that child's development shall be guilty of an offence and liable on conviction on indictment to a period of not more than ten years imprisonment, and a fine".
The proposed amendment would also give as defences for anyone charged under the law "that the act or acts ending the life of an unborn child were lawfully performed at premises operated by a Health and Social Care Trust", or "that the act or acts ending the life of the unborn child were lawfully performed without fee or reward in circumstances of urgency when access to premises operated by a Health and Social Care Trust was not possible".
The move comes ahead of draft guidelines on abortion going before the Northern Ireland Executive next week.
Legal action taken by the Family Planning Association against the Department of Health, in a bid to have the guidelines published, was halted on Wednesday after confirmation of Health Minister Edwin Poots's position on the issue.
Mr Poots is now to submit a paper seeking approval to go out to public consultation.