The 23-year-old, a January signing from Coventry, made 13 appearances for the Magpies last season (seven of them as a substitute) but is still waiting for his first goal for the club.
Trapattoni used him as a substitute in the World Cup qualifiers against Italy and Montenegro, the first leg of the play-off against France and March's friendly clash with Brazil.
Best, who hopes to be included in the full squad for next week's friendlies against Paraguay and Algeria, is at the Irish training camp trying to impress.