Fulham have agreed a fee with Rangers for the transfer of Steven Davis and with Ipswich Town for Moritz Volz.
The Ibrox club were keen to secure Northern Ireland international Davis on a permanent deal following a successful loan spell in the latter part of last season.
The move was thrown into doubt over the summer when both clubs failed to reach agreement over the midfielder's value.
But Gers manager Walter Smith has revealed that Davis is now close to putting pen to paper following months of protracted wrangling.
He said: "We have reached agreement with Fulham and we still have one or two things to settle with the player and his representatives but we are hopeful that one will go through.
"That should happen in the next couple of days.
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"It's a transfer that has been really ongoing so we don't want to count our chickens.
"But we have agreed with the club now, which is a big thing, and we would hope we can reach agreement with Steven's people over the next couple of days."
Fulham confirmed a fee of around £3million had been accepted but said the deal is still subject to personal terms being agreed.
A spokeswoman explained: "Steven came up with us [prior to the match with Hull City] but then went up to Glasgow to speak to them and he's now back in London."
Meanwhile, Ipswich Town are to hold talks with the Cottagers' Moritz Volz after a bid was accepted for the full-back.
Volz has struggled for regular first-team football at Craven Cottage since Roy Hodgson's arrival as manager. Hodgson is happy to allow the German to move on after improving his defensive options over the summer, with the fee reported to be £500,000.
Speaking after Ipswich's 3-0 win at Burnley on Saturday, Town manager Jim Magilton confirmed he is hoping to sign Volz.
"We have made an offer to Fulham for Moritz Volz and it's been accepted," Magilton said.
The right-back has spent five years at Fulham after originally joining the club on a loan basis from Arsenal.