Inquiry about a product in a store for online purchase.

Is it permissible to enter a store, ask for a recommendation about a product to see a good model, and buy it cheaper online?

If his intention is that if it is cheaper, or if the difference is not significant, and he has a chance to buy through him, there is no prohibition of verbal deception. However, if his intention is not to buy from this seller at all, it is forbidden due to verbal deception. It is also forbidden due to theft since he enters the store, and presumably, the store owner does not agree to people entering his premises for price comparison. If he tells him from the start that he did not come to buy but only to look, there is no prohibition.

It is stated in the Gemara, Tractate Bava Metzia, page 58b: "Verbal deception is greater than monetary deception, for it is said regarding it: 'Fear your God,' and regarding the other, it is not said: 'Fear your God.' Rabbi Elazar says: this concerns one's body, and this concerns one's money. Rabbi Shmuel bar Nachmani said: this can be restored, and this cannot be restored."
And it is written in the Shulchan Aruch, Choshen Mishpat, Siman 228, Paragraph 4: "What is verbal deception? Do not say: 'For how much do you want to sell this item?' if you do not intend to buy it."
However, if his intention is to buy if it is cheaper, certainly there is no prohibition of verbal deception in price comparison before purchasing.