If a professor says he will not fund my internship as it will be my first visit, how can I convince him politely? I contacted a professor in a foreign university for a possible research internship in his lab. He is willing to accept me as an intern, but has stated that since he barely knows me and it is the first time I will be working under him, he will not provide any financial support.

I have read his publications, his areas of interest match with mine, and I believe that his papers were among the most exciting ones I have read so far. Being an undergraduate, I have limited funding of my own and I don't want to miss this opportunity because of lack of resources.

Since he mentioned 'will not fund' instead of 'cannot fund', I feel that there is some scope to convince him. Can someone advise me regarding what I should say to do so, without being rude? I would appreciate any help.
It may help to look at this from the professor's point of view:


You are not a student at his university (or even a citizen of his university's country), so internal research grants are not an option (indeed, he may face some backlash for hiring a non-student if research slots are limited).
You are an undergraduate, so your ability to be useful to him is very limited, especially at first as you are ramping up. (Undergraduates generally have limited time and skills compared to grad students and post-docs). 


Given this, his position is quite reasonable: if you want to work "for free", fine; otherwise, this won't work out. 

To change his mind, you need to reverse one of these assumptions:


You can find a pot of money (e.g., a scholarship) and ask for his support in applying for it
You can prove that you are really useful for the lab, and that paying you a meager salary is more cost-effective than other options. But, for most undergraduate students, this will be an impossible sale, and the professor will quickly tire of saying "sorry, no."


In short: I really don't think you'll be able to convince him. Your best bet is to look for scholarships or other funding. If that doesn't work out, you should tell him honestly that while you appreciate his offer, and would certainly accept it even with a modest stipend, you simply cannot afford to travel to and live in the foreign country with no income.