Barry, who turns 16 today, is now available to be poached by European clubs and has been linked with Spanish giants Barcelona.
But the Baggies have offered him a one-year scholarship followed by a two-year professional contract that kicks in when he turns 17.
EFL rules state: “Your club may offer you a professional contract to commence from the age of 17 at any time from 1st January following the commencement of your under 16 year.”
Barry, who has been honed by the Baggies since the age of six, is a prolific striker from Sutton Coldfield who has caught the eye while playing for England’s youth teams.
He rose to prominence last year when he scored 10 goals in five games for England Under-15s at a tournament in Italy.
He also won the golden boot in November at the Val-de-Marne tournament which England Under-16s won.
Fifa rules forbid players under 18 moving to a foreign club but those aged 16 and 17 can move within two countries in the European Economic Area.
If academy players move from one English club to another, compensation is determined by a tribunal, but if they move abroad, Fifa's flat rate for compensation of £235,000.
The Bishop Walsh Catholic School pupil is rumoured to be interesting a number of overseas clubs, and Barcelona have been linked with him.
However, Albion are currently expecting the young striker to return to training on Monday with the rest of the players in the academy and senior squad.
And they are looking to tie down one of their most promising youngsters with a new deal.
Albion’s transfer activity is expected to crank into gear next week when Slaven Bilic starts his stint as head coach.
The Baggies are interested in Arsenal right-back Carl Jenkinson, although he’s believed to be one of a number of players being considered.
Albion will need at least one right-back this summer after loanee Mason Holgate returned to parent club Everton.
Allan Nyom, who spent last season on loan at Leganes, is expected to be sold this summer because he has one year left on his contract.