Rice is understood by Standard Sport to be a top priority for the Gunners, with a price tag of around £120million in the offing and talks set to begin after the Hammers’ Europa Conference League final next month.
However, competition for the England star is likely to be high with Johnson tipping Paris Saint-Germain, Manchester City and Bayern Munich to all join Chelsea in outbidding Arsenal should they want him - with the west Londoners holding the advantage in the form of Rice’s longtime pal Mount.
“Right now he is hot property and there are so many other teams who are going to want him,” he told opinion website Lord Ping.
“Arsenal are not going to be able to compete financially when it comes to salary or transfer fees against City or Bayern or PSG - it is just not going to happen.
“I think he would be a great fit at Arsenal because he has the technical ability and he would suit that team down to the ground. But, if he is available, then the bigger teams are going to take him.
“I think Rice is more likely to go to Chelsea than Arsenal, especially if Mount stays. They are obviously good friends, they go way back.”
Mount is entering the final year of his Chelsea contract with his future far from resolved.
Liverpool, Manchester United and Arsenal have all been linked with the midfielder and Johnson believes the Gunners are best placed to do a deal if he moves.
He added: “Mount to Arsenal is probably the most realistic transfer out of all those scenarios. He is another fantastic player and he would suit that team down to the ground and he would probably cost half the money.”