The phrase "a note suggesting that" is correct and usable in written English.
It can be used when you want to indicate that a note contains a recommendation or proposal regarding a particular matter.
Example: "In the meeting, I received a note suggesting that we consider alternative suppliers for our project."
Alternatives: "a memo proposing that" or "a message indicating that".
Citigroup put out a note suggesting that, as far as the level of the FTSE 100 went, there was "much in the price already for the risk of global recession" and maintained its target for the end of the year - 6,200.
Half hidden among the pile of papers is a bulky parcel containing five volumes which his editor has sent with a note suggesting that they "ought to go well together".
That, he says, led her to write a note suggesting that JonBenet had been kidnapped, after which she "faced the major problem of what to do with the body".
The first item on the page was a note suggesting that the executives should tell the government officials that Bank of America was considering backing out of the deal, said one of the people with knowledge of the matter.
On its website is a note suggesting that a 2% annualised fall in its indicator over a six-month period, with more than half of the components worsening, provides a reliable though not perfect warning of recession.
Whenever I get an email from the institute, several of my Guardian colleagues receive one too and regularly forward their copies to me - sometimes with a note suggesting that I might like to check out the story and write about it.
Writer ends on a hopeful note, suggesting that ospreys may be making a come-back, possibly because less DDT is reportedly being used.
Speaking to the Guardian on Friday, Ernesto Ferrero, the book fair's artistic director, struck a conciliatory note, suggesting that discussions concerning Saudi Arabia's status as a guest of honour had "never reached the level of a formal agreement".
Unfortunately, the III turned out to be a manufacturing calamity, and at one point Apple issued a technical note suggesting that customers could make the machine work by simply dropping it three inches onto a desktop in order to reseat chips that would come loose.
I end with an optimistic note, suggesting that even a CFPA with less power than envisioned in the proposed Act could do much good.
They said they would remain in touch and had parted on friendly terms -- a grace note suggesting that the negotiations, which have been through uncounted ups and down, might be rekindled.
