You have given very little information about this job so the simple answer is NO, but this is on the assumption that you are referring to painting directly over the varnish with an emulsion coloured matt paint that is water based.
Are we talking a simple bath panel? or a large wood panelled drawing room with chintz curtains !!!
As a general rule, for the first coat you will need a paint that has better 'sticking' qualities than an ordinary matt emulsion, it will paint on but it will soon start to breakdown and most likely peel or flake off later on.
If the varnish is good and sound then start by sanding the panels using either a 100 grit or 120 grit paper to key over the surface. This will provide a good base for a first coat of paint which needs to be a primer. If it were I doing the job, then I would use either Zinsser BullsEye 1-2-3 or an Oil based primer and then when completely dry of at least 24 hours later, apply your matt paint.
If however this is just a quick DIY job of no importance , then you could use the Dulux Trade quick drying wood primer undercoat after sanding down, then go on to your matt paint. You may just get away with doing this unless the varnish is already peeling and flaking off.
I would use Zinsser 1 2 3 as oldgreymouse says or E S P (easy surface prep) made by Owatrol. Sand first to remove loose varnish then follow instructions on tin, wipe off after about 5 mins and paint after 2 hours as I recall. I did it on some varnished built in furniture some years back and it lasted well.
footprints
If you need to find a tradesperson to get your job done, please try our local search below,
or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Please select a service and enter a location to continue...
Are you a trade or supplier? You can create your listing free at DIYnot Local