'suggest improvement' is correct and can be used in written English.
Example Sentence: Management has asked staff to suggest improvement ideas to increase productivity.
There is experimental evidence that thiazolidinediones improve fibrosis, and clinical studies suggest improvement in liver enzymes (62).
They measure health professionals' performance against clinical guidelines, and some systems suggest improvement actions.
Results suggest improvement in skill accuracy in both the training and generalization settings.
She'll find, firstly, that the data are not very good, and secondly that some measures suggest improvement and some stasis or deterioration.
The results of neuropsychological evaluations before and after therapy suggest improvement in executive functions and better self-esteem.
The manager is told that he is to recognize good work, suggest improvement, get agreement on top priority elements of the task, clarify responsibility, verify and correct rumors, and talk about personal and long-range goals.
