If you make it a smart object (dropping the image onto the canvas or right clicking) you will be able to scale the image without a loss of clarity.
When saving files, use JPEG for something you plan to upload, PNG for printing, and TIF if you want to edit it and be able to look at it without any compression.
Thank you Nexahs1138 for your prompt reply. I did the following steps -
1. Right clicked the image in AI
2. Dragged the corners to reduce the size of the image and
3. Export as JPG.
With this the image became decolored and blur, but did not impact the size. Please refer to the attached the before and after screenshots from LinkedIn page.
If you are editing an already created image from a file then you would be better off doing this in Photoshop as that is for editing pictures with bitmaps as opposed to Illustrators vector lines.
I may be wrong in guessing this isn't possible in Ai as I don't use it for editing but if you do this is Photoshop it should work no problem.