Lukaku has scored 13 Premier League goals for West Brom this season after being allowed out on loan by Chelsea to gain first-team experience in England.
He was also a target for Stoke, but Potters boss Pulis feels his West Brom counterpart Steve Clarke's Chelsea connections made the difference.
"I spoke to Chelsea first-team coach Steve Holland," said Pulis. "He was very complimentary about Romelu and we wanted him.
"Unfortunately, there were plenty of other people who knew about him, too. I think West Ham and Fulham were in there.
"But Steve got him on loan because of his connection with Chelsea.
"Romelu's a good signing and has got better as the season's gone on."
Belgium international Lukaku is expected to start for West Brom against Stoke at the Britannia Stadium on Saturday.