No ruling yet ... but it's close. 

The NFL Player's Association has said the arbitrator overseeing Ezekiel Elliott's appeal of his 6-game suspension was trying to issue his decision by end of business day on Tuesday -- but so far, nothing yet. 

The operative word in that sentence is "trying" -- we're told the arbitrator has a lot of material to comb through and wants to be thorough ... he doesn't want to rush out a decision. 

Meanwhile, Ezekiel appeared in a courtroom in Sherman, Texas where he filed documents in federal court asking for a restraining order against the NFL, barring the league from enforcing punishment stemming from the domestic violence investigation. 

Stay tuned ...