Allardyce thinks Johnson, 25, is the best English scorer he can find, although Palace may not let him go for less than £8m.
Palace chairman, Simon Jordan, has already shown he is prepared to play hard-ball by dismissing a reported £6 million bid from Everton as "not enough to buy his trainers".
"AJ will be starting next season with Crystal Palace," Jordan said. "Apart from anything else it makes sound business sense."
Meanwhile, according to reports today, Quinton Fortune is poised to join Wanderers by the end of the week, while the Trotters are also being linked to another keeper in the form of Deportivo La Coruna stopper Jose Molina.