The Transocean Winner rig was blown ashore in severe weather conditions on the western side of the Isle of Lewis last week when it detached from its tug en route from Norway to Malta.
A 300-metre sea and air exclusion zone is in place around the semi-submersible which grounded at Dalmore beach near Carloway.
Duncan MacInnes, of the Western Isles Fishermen’s Association, said four boats would normally work in the exclusion zone.
He said “This is the time of year when lobster are most plentiful in shallower grounds.
“Fishermen in Shetland got compensation when the Braer went down and we would insist on a similar compensation scheme for our members.”
The Braer oil tanker ran aground on Shetland on 5 January 1993, spilling almost 85,000 tonnes of crude oil.
The Transocean Winner was carrying 280 tonnes of diesel when it ran aground and salvage teams have since discovered two of its four fuel tanks have been breached.
The rig is believed to have leaked 44 tonnes of diesel fuel, most of which is thought to have evaporated, as only a “low” level of pollution was detected when it ran aground, daily searches have found no further traces of pollution.
Teams plan to transfer the remaining 137 metric tonnes of diesel fuel – a light and non-persistent oil with lower environmental risks than heavy black crude oil – in the intact tanks to tanks above the waterline.
A Maritime and Coastguard Agency spokeswoman said an underwater survey on the rig continued yesterday.
She said: “The survey is assessing the damage and looking at the possible refloating routes for the rig.
“A team of salvors remains on board continuing its assessment of the damage and also working to make connections for the towlines.
“It’s expected that by the end of the day the team number will have increased to 15.”
She warned any aircraft or drone that breaches the new air exclusion zone around the rig will be prosecuted.
Hugh Shaw, the Secretary of State’s Representative for Maritime Salvage and Intervention, said: “The exclusion zone has been put in place for the safety of the operational aircraft working at the scene and also for the teams carrying out their surveys and assessments.”