I have a good memory of reading such a thing in one of the (many) books on D-Day that I have read down the years. As I recall, the British advised the Americans not to undertake a frontal assault because the defences were too strong, and it would be a bloodbath.
Omaha certainly was a bloodbath.
Is my memory correct? Were the Americans advised not to assault Omaha?
I've never heard of anyone in the British military directly advising the Americans not to land at all at Omaha. The difficulty of the landings at Omaha was caused by a number of factors, many of which could not have been predicted or were planned for, but went awry (such as the complete failure of the bombing on that particular beach).
What the British did do, though, was offer the Americans some of their "funnies" - special tanks designed by the Royal Engineers, specifically for the task of clearing beaches under fire. They had minesweeper tanks, super heavy tanks with heavy duty artillery on board to destroy strongpoints, and flamethrower tanks. They also had amphibious tanks, which were the only ones the Americans used on their beaches (and on Omaha, almost all of them sank, mostly due to being let out too far from shore in very heavy seas).
So I while don't remember ever reading that the British advised against attacking at Omaha, they did make at least one recommendation that the Americans then ignored. Whether the funnies would have helped enough to change the outcome is impossible to say, of course.
Source: Omaha Beach, a Flawed Victory by Adrian R. Lewis
Were the Americans advised not to assault Omaha?
Absolutely not.
In fact Omaha was the key that bound the British and Canadian beaches (Gold, Juno and Sword) to the other American beach, Utah.
The plan that eventually became Operation Overlord originated in May 1943 when British general Frederick Morgan was ordered to start detailed planning for a cross-channel invasion. The initial plan was for a three-division assault in the area of the British and Canadian. This smaller plan was mostly the result of planning around the expected number of landing craft that would be available.
When Montgomery was appointed commander of the land forces for the invasion he very quickly realized that the planned area was much too small and might easily be contained by the Germans. Together with Eisenhower, he pushed for a larger force over a wider area. In particular they wanted an assault on the Cotentin peninsula to cut off the troops there and make an early push for Cherbourg.
If troops were landed on the Cotentin then the area between the British and Canadian beaches had to be taken. And that meant landing at the beach now known as Omaha.
Incidentally it was not until a week or so before the invasion that Allied command uncovered that the 352nd Infantry Division had taken over responsibility for the Omaha area. The 352nd was a regular army unit with a good number of Eastern front veterans in its ranks. The unit it replaced, the 716th Infantry Division, was a 'static' unit lacking in mobility, heavy weapons and training. Had the assault taken place against the 716th the casualties at Omaha might have been more comparable to those at Gold-Juno-Sword.
edit to add source : Joe Balkoski, Omaha Beach