Tunnel camera footage was published after the Reds' hard-fought 3-2 victory over the Hammers on Monday night.
Van Dijk, who already looked angry at a performance in which Liverpool conceded two goals against a side in the relegation zone, shrugged off Soucek's request for his shirt.
The footage, which starts at 12 minutes 11 seconds, sees the Dutchman walking down the tunnel only to be asked "Virgil! Can I get your shirt?"
But Soucek looked disappointed to hear van Dijk say "I've already given it to him," while pointing to Pablo Fornals and then swapping shirts with him.