1.
If someone talks up a particular thing, they make it sound more interesting, valuable, or likely than it originally seemed.
Politicians accuse the media of talking up the possibility of a riot...
PHRASAL VERB: V P n (not pron), also V n P
2.
To talk someone or something up in negotiations means to persuade someone to pay more money than they originally offered or wanted to. (mainly BRIT)
Clarke kept talking the price up, while Wilkinson kept knocking it down.
PHRASAL VERB: V n P, also V P n (not pron)