The attacking midfielder, who is widely regarded as one of the best players in the Championship, is set to leave the Royals as a free agent at the end of the season.
Manager Steve Bruce is determined to oversee a large squad overhaul if he remains in charge at The Hawthorns next season.
It’s not known if Albion have decided to pursue a move for Swift having sent scouts to watch him on a number of occasions.
But the 26-year-old does now seem highly likely to be a Baggies target this summer.
Bruce has gone on record to say he is determined to add more flair to the his under-performing squad. He is also keen to exploit the free agent market.
Swift would provide some much needed creativity in the middle of the park. The former Chelsea man is comfortable playing in central midfield and in the number 10 role.
And despite playing for a Reading side that has battled relegation all season, he has managed to score 11 goals and register 13 assists this term.
Swift is unlikely to play for the Royals again this season after hobbling off injured against Cardiff earlier this month.
Albion, though, are sure to face competition to land Swift, who has been linked with a move Leeds. Burnley and Brentford are other sides reportedly keen on the former England under-21 international.