Newcastle and Everton have both made £6million-plus bids for the Lambeth-born player with the Magpies confident of luring him north. Reports this morning even suggested Parker was due in Newcastle today to meet with club officials.
If Parker spurns Newcastle and Merseyside for north London, a settlement could be reached this week. If not, further talks between Spurs and Chelsea are planned.
Meanwhile, Tottenham and Liverpool are leading the chase to sign Fulham midfielder Steed Malbranque after the Frenchman ruled out the prospect of playing for Aston Villa.
The Birmingham club have bid around £3.5m, but Malbranque said he had no interest in joining David O'Leary's side.
Malbranque's snub to Villa has paved the way for both Spurs and Liverpool to step up their interest in the midfielder, who arrived at Fulham from Lyon for £4.5m four years ago.
The Frenchman is a big favourite with Fulham supporters, though he failed to capture his best form last season, partly due to injuries, and was left out of the squad altogether towards the end of the campaign.
However, Fulham manager Chris Coleman regards him as a key part of his plans for the new season and is hoping to combine the 25-year-old with Papa Bouba Diop and Claus Jensen in central midfield.
Coleman will be encouraged by Malbranque's decision to resist Villa's overtures, though it is unlikely that the Frenchman would turn down the chance to join the European Cup winners or Spurs, both of whom are expected to bid in the next few days.