Croatian international Orsic, who’s scored 11 goals in 13 league games this season, had been club’s No 1 target, with West Brom submitting a second bid of €8m plus a further €1m add-ons for the winger.
However, West Brom were unable to agree personal terms with the 27-year-old, while Zagreb were still hoping to secure a further €1m in add-ons.
Grosicki, whose contract expires in the summer, is a cheaper alternative as Slaven Bilic looks to add a winger before the deadline closes on Friday.
West Brom have agreed a fee for the 31-year-old, who has been a regular starter for Hull since joining from Rennes in 2017 and has scored seven goals in 28 appearances this season.
It’s understood that Crystal Palace’s attempt to sign Jarrod Bowen is unlikely to affect West Brom’s approach, with Hull preferring to sell now than lose Grosicki for free in the summer.
Bilic has also already added striker Callum Robinson on loan from Sheffield United this month as the club chase promotion from the Championship.
The Baggies have lost three of their last five games, relinquishing their lead at the top of the table to Leeds, while Grady Diangana is recovering from a hamstring injury.