Yes your washer can be the culprit - lint comes off in both the washer and dryer.
We wash whites on hot, then run the machine empty on cold (to remove any oxyclean or bleach or bluing that may remain in the tub), then we do our dark clothes, then our sheets and then the towels (towels leave the most lint BTW) and then the animal sheets (which we use to cover the furniture) which has a great deal of animal hair - then we run the washer through a cold empty cycle.
Doing it that way we have reduced the amount of lint (and animal hair) in the darks and on the sheets.
Other things that play a roll on how much clothing you stuff into a wash load, how much clothing you stuff into a dryer, the kinds of material of the clothing (such as towels - the terricloth creates loads of lint which can be stuck inside th machine for the next load of clothing).
The Wash machine needs to be cleaned periodically too.
If you use the center part for fabric softner, fabric softner can be gunking up the water line area and above - Fabric softener is spread by the first spin cycle and doesn't get washed off the walls when the machine refills Washing and agitation of a load of clothing could cause linty water to lap up leaving lint onto the sticky residue.
These liquids and mineral deposits can reach up all the way under the lip of the machine (where you can't see it) and can get caked with lint, dust and what not which could drop back into the machine on the final cycle and get onto your clothing.
Does yor machine have lint traps? Older machines used to have this tray that sat on the agitator (the center pillar of the machine) where a ball of lint would collect as the water cycled through, newer machines place that else where different machines put them in different places.
http://www.friendlyplumber.com/plumbing101/how_tos/washing_machine_cleaning.html goes more indepth on cleaning a washing machine.
I hope some of this helps, I tried to cover all bases.