The January signing from Besiktas struggled for a first-team place in the opening weeks of his Everton career with Allardyce saying he would not rush him as it took time to adjust to life in the Premier League.
In recent weeks though, Tosun has started to establish himself as Everton's main striker, netting four goals in the last four games, and the 26-year-old insists that he is a big fan of Allardyce.
He said: "I get on really well with Big Sam.
"He's been in contact with me for a long time and wanted me when he was at Crystal Palace. He made it clear there would be a place for me at Everton.
"Sam played an important role in the transfer. He was always open with me, he doesn't mince his words, he says what is on his mind."