The Gunners moved to within one point of the top four with a narrow victory away at Huddersfield on Saturday as goals from Alex Iwobi and Alxander Lacazette secured a 2-1 win.
Unai Emery's side kept pace with Manchester United, who earlier on Saturday jumped to fourth with a comprehensive win over Fulham, though Chelsea will reclaim their spot with victory at Manchester City on Sunday.
Despite such fine margins, Souness is adamant the battle for fourth is a "straight fight" between Manchester United and Chelsea, ruling out Arsenal's chances of outperforming both between now and May.
He wrote in the Sunday Times: “It’s a straight fight between Chelsea and Manchester United for fourth now, but Chelsea will be looking over their shoulders because United are dangerous and, right now, the momentum is there with them and they are on a roll.”
EPL table | As it stands
It highlights a remarkable turnaround under Ole Gunnar Solskjaer for United, who were 11 points behind the Blues when Jose Mourinho was sacked just before christmas.
But Souness has warned the signing of Gonzalo Higuain could swing momentum once more in this season's topsy-turvy race for a Champions League spot.
He added: “Chelsea will win more games with Higuain scoring goals for them,” Souness continued, “but we will have to wait and see if he can take them to fourth place.”