Arbitrators Margaret Brogan, Andrew Strongin and Gil Vernon are expected to decide the case Tuesday, a day after hearing arguments.
Pham hit .275 with 21 homers and 63 RBIs for St. Louis and Tampa Bay, which acquired him on July 31. He batted .343 with seven homers and 22 RBIs in 39 games for the Rays.
He set career bests in 2017, when he hit .306 with 23 homers and 73 RBIs.
Players and teams have split the two decisions thus far: Oakland closer Blake Treinen won at $6.4 million rather than the team's $5.6 million offer, and Washington outfielder Michael A. Taylor lost and was awarded $3.25 million instead of his $3.5 million request.
A decision also is expected Tuesday for Houston shortstop Carlos Correa, whose case was heard last week.
Eight players remain scheduled for hearings through Feb. 15.
Houston reliever Chris Devenski avoided a hearing when the team announced a deal Monday for a one-year contract worth $1,525,000. The agreement contains a $2,625,000 team option for 2020, and the option price could escalate based on games this year: $2,725,000 for 50, $2,825,000 for 60 and $2,925,000 for 68.
Devenski's agreement is at the midpoint of the $1.4 million the 28-year-old right-hander asked for and the $1.65 million he had been offered.
He was 2-3 with a 4.18 ERA last year, striking out 51 and walking 13 in 47 1/3 innings. He was sidelined between July 27 and Aug. 30 because of left hamstring tightness, the first time in his big league career he was on the disabled list.
He had a $599,200 salary last season and was eligible for arbitration for the first time.