The proposed remedy has been tabled by the companies after the UK's Competition and Markets Authority (CMA) raised concerns that a deal to bring AFW under the control of Wood Group could lead to "a substantial lessening of competition" in the market for those services in the UK.
The CMA announced earlier in August that, as a result of its concerns, it would open a full-scale competition investigation into the proposed £2.2 billion takeover of AFW by Wood Group unless the companies put forward plans which would address its concerns.
In its latest statement, the CMA said that "there are reasonable grounds for believing" that the proposals put forward by Wood Group and AFW, "or a modified version of them, might be acceptable". It said it would consult stakeholders on the proposals before reaching a final decision.
A provisional deadline of 12 October applies for the CMA to make its decision, although it could extend the deadline back to 7 December in "special circumstances", it said.
Kate Collyer, deputy chief economic adviser at the CMA and decision maker in this case, said: "It is crucial that competition is maintained in this major UK industry. We will consider the undertakings offered by Wood Group and Amec Foster Wheeler further, and carefully consult interested parties, in order to make sure that they fully address our concerns."