Absolutely. PROCESS is based on OLS regression/General Linear Modeling. You can use Hayes' book on PROCESS as reference (see link), if a reference is really needed. Andy Field's Discovering Statistics Using SPSS 4th ed. also discusses this from what I remember.

It's actually more of a "system" of regressions.

For example, for a simple mediation of X->M->Y, you have (excuse the non-math ability of the textbox):

• M ~ b0M + b1M*X  (so a simple regression with X as a predictor)

&

• Y ~ b0Y + b1Y* X + b2Y*M (so a multiple regression with X and M as predictors)

Then the direct effect is b1Y , and the indirect is (b1M * b2Y).

I would use his book as reference (see link), though honestly, most (if not all) path analysis (mediation, moderation, etc.) with (assumed) normally distributed outcomes use OLS (e.g., the R package Lavaan), as the only option, or at least as default.

http://afhayes.com/introduction-to-mediation-moderation-and-conditional-process-analysis.html

I am using both Hayes' and Field's books. I just couldn't find the answer to my particular question, as Hayes is really not understandable for me and Field do not cover mediation.

Thank you very much for the answer.

You're right it's not very explicit. Here page 6 talks about mediation as "linear models", might help.

http://is.muni.cz/el/1423/podzim2014/PSY704/50497615/hayes_2012_navod_process.pdf

Oh yes, I think I've read through million of Hayes' publications, and he always says linear regression, but not really if it is simple or multiple (with multiple IVs). 

Thank you for your help.

It is multiple. I think he felt he was conveying that in the formulas, but it is never made explicit. That does mean the regression weights are contextual, not zero order.