The Israeli offer, broached by envoys in Geneva over the weekend, included measures for patching up ties but appeared to have fallen short of Turkey's demand that Israel formally apologise for the deaths of the nine peace activists in May.
Israeli Prime Minister Benjamin Netanyahu, who sent a delegate to a UN probe of the bloodshed, also faces opposition to such a deal from his hawkish foreign minister and government coalition partner, Avigdor Lieberman.
"We made a compensation offer, and asked the Turks to do what needs to be done to address our legal concerns. We also want to see them return their ambassador and allow us to appoint a new ambassador in Ankara," an Israeli official said.
"For now, however, there are still big obstacles."
The draft offers Turkey some $100,000 each to families of the men shot dead by Israeli marines during the deadly raid of the converted cruise ship Mavi Marmara, and an Israeli expression of "regret" over the incident, Israeli diplomatic sources said.
Turkey's Foreign Minister Ahmet Davutoglu described the reports of an Israeli offer as "speculative" and said on Thursday his government's demands had not changed.
"We don't think it is right to cite figures, or discussions of apology or regret," Davutoglu said during a joint news conference with the visiting Syrian foreign minister.
"The citing of figures or the matter of regret did not come onto the agenda."
On Wednesday, Netanyahu adviser Ron Dermer said Israel and Turkey were discussing "the phrasing of a compromise that both sides can live with ... (and) that will get our relations with Turkey back on track and remove the whole affair from the international agenda".
Rattled over private war-crimes suits filed abroad against its military brass and politicians, Israel has tried to stave off any similar Turkish actions in global forums by quickly setting up two internal investigations whose findings will become its submission to the UN inquest. Turkey has dismissed the Israeli probes as insufficient.
In September, a UN Human Rights Council investigation claimed that Israel's military broke international laws during its raid on the Gaza-bound aid flotilla. The report stressed that the action by Israeli commandos was "disproportionate" and "betrayed an unacceptable level of brutality", as related by the BBC.
The UN report went further to indicate that there was clear evidence to support prosecutions against Israel for "wilful killing".
Israel dismissed the probe as "biased" and "one sided".