forecasting - likelihood of customers participating in next month sales
Forecasting is about predicting a variable as a function of time, such as the number of sales during coming months). Your problem is a regression problem, where the output is between 0 (no chance) and 1 (certain).

Any method to solve a regression problem is valid, but I would recommend starting with the simplest thing you think may work, to establish a baseline performance that you can try to improve.

This problem is often phrased as churn prediction, which is just the opposite chance from what you need (although definitions of churn vary), so you can google and see how people do that.

One easy approach that allows you to calculate this is to use the RFM model, where R, F and M stand for recency (time since last purchase), frequency (of purchases) and monetary (total money spent). You could use these features and a logistic regression as your baseline model.