The United States international has, at just 20 years of age, established a reputation as one of the finest young talents in world football.
So impressive has his progress for club and country been over recent years that a scramble for his signature was always expected to be sparked at some stage.
The current transfer window has seen an agreement finally reached, with Chelsea having moved quickly to fend off interest from domestic and European rivals to secure the services of a much sought-after talent.
Pulisic will link up with the Blues over the summer, with his arrival at Stamford Bridge set to leave others disappointed – particularly Spurs, who opted not to bolster their ranks last summer and have now seen a potential winter target head elsewhere.
Quizzed on whether he expects any January moves to be made by Mauricio Pochettino, former Tottenham boss Redknapp told talkSPORT: “I’ve got a feeling, I don’t think they will.
“I heard they were interested in the boy who went to Chelsea [Pulisic]. He was on their radar but was too expensive.
“I think they will stick with what they’ve got.”
Spurs have fared admirably this season despite bringing no fresh faces onto their books.
They sit third in the Premier League table at present, with just six points separating them from leaders Liverpool.
Redknapp believes a title bid may be beyond Pochettino’s side, but feels a top-four finish and a trophy are there to be shot at – with Tottenham preparing to open their FA Cup bid for 2019 against Tranmere before then turning their attention to a Carabao Cup semi-final tie with Chelsea.
“It’s all become about the top four now,” Redknapp added.
“No disrespect - we see the cup competitions, with the FA Cup teams get to the quarters and put half a reserve team out.
“I think it would be nice to see Tottenham win a trophy. They should go for it.
“Chelsea next week - that’s a big game. Go to a final, go win a trophy.”