The Baggies have already held preliminary discussions with Cowley and are planning a second round of talks this week, Press Association Sport understands.
Middlesbrough hold an interest in Cowley after they parted company with Tony Pulis, but Albion are further down the line with their search.
The 40-year-old would cost the Baggies £500,000 under the terms of his contract at Sincil Bank, which has another three years left to run.
Norwich, Nottingham Forest, Ipswich and Barnsley have all previously looked at Cowley and his brother, assistant Nicky, with the pair having taken Lincoln from the National League to Sky Bet League One in three seasons.
The Imps won Sky Bet League Two this season, having been promoted back to the English Football League in 2017.
Former Brighton boss Hughton is under consideration by West Brom after he was dismissed by the Seagulls last week.
Hughton has won promotion to the Premier League with Newcastle and Brighton but was axed after the Seagulls, who have appointed Graham Potter, survived by a narrow margin this season.
Albion's next appointment would be their fourth manager in just over a year.
Having sacked Alan Pardew in April 2018, Darren Moore was then dismissed in March and Jimmy Shan appointed caretaker. Shan stayed in the role until the end of the season after Albion failed to land Preston's Alex Neil.
They finished fourth in the Sky Bet Championship but lost on penalties to Aston Villa in the play-offs.
The Baggies are keen to make an appointment in the next few weeks to give the new boss as much time as possible to rebuild the squad ahead of next season, but they do not want to rush into one.
Sporting director Luke Dowling has confirmed they aim to talk to all four candidates in the next two weeks.
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