West Brom are hoping to secure the services of loan duo Juan Carlos Menseguez and Youssouf Mulumbu on permanent deals.
Baggies boss Tony Mowbray landed the duo from San Lorenzo and PSG respectively during the winter transfer window with a view to full-time terms being agreed in the summer.
Both men needed time to find their feet in the Premier League but improved enough during the closing stages of the campaign for Mowbray to believe they are worthy of extended stays.
The Hawthorns boss must now convince his board to find the funds to finance the deals so that the duo can become part of the club's Championship promotion push next term.
"I would hope that both players could be signed up. I can only go to the board and give my opinion on what I think should happen," Mowbray said.
"There was a difficult period for both players when they came and neither found it easy with the pace of the game or the physicality of the game.
"But both have now acclimatised and I think they are at the stage now where they can only push on and get better. My opinion is we should try and take up the options with them and get on with it.
"I think they are both tied in with us as long as we pay the money we have agreed with the two clubs."
Striker Menseguez started to feature more prominently in the final stages of the campaign.
Mulumbu, 22, was initially unable to play a part because of injury but has added some much needed bite and steel to the West Brom midfield.