The 6ft 3in centre half trained under David Moyes' supervision and played 90 minutes of a reserves match, but is due to return to his club Nafthan Novopolotsk.
No hurry: Verkhovtsov will make a decision on his future at the end of the season
Verkhovtsov had a similar trial at Celtic last year but failed to clinch a £500,000 transfer, instead moving to Latvian side Ventspils in January only to see the deal cancelled in a contractual dispute.
The 24-year-old has become a regular at the heart of Belarus's defence since making his international debut in 2008 and is highly regarded in eastern Europe.
Verkhovtsov impressed against England at Wembley last year despite being on the wrong end of a 3-0 defeat and would have no problem getting a work permit.
Explore more:People: David Moyes Places: United Kingdom