Morita, a 30-year-old Japanese international with 40 caps for his country, was a target for Leeds United last summer ahead of their Premier League return but opted to see out the final year of his Sporting contract.
His consistent form during Sporting's run-in has prompted calls from supporters in Lisbon for the club to offer him a new deal, but Leeds are understood to be leading the chase and the midfielder is willing to commit once the club secure their survival.
Doekhi, 27, will be a free agent this summer when his Union Berlin contract expires. The Dutch defender, who is a nephew of former Chelsea centre-back Winston Bogarde, has been a consistent performer in the Bundesliga and has attracted interest from Borussia Dortmund as well as Leeds, who made enquiries earlier this year and remain in contention.
Leeds sit six points ahead of Tottenham Hotspur in the table with four matches to play, facing already-relegated Burnley on Friday before a crunch trip to Spurs on 11 May. A home match against West Ham United, who are also fighting for survival, closes the season.
Both signings would address specific needs: Morita would provide experienced competition for Welsh international Ethan Ampadu in midfield, while Doekhi would bolster a defence that has been tested throughout a demanding debut season back in the Premier League.