Manchester United boss Ole Gunnar Solskjaer and Tottenham chief Jose Mourinho paid tribute to the defender after winning his battle with cancer as a teenager.
Taylor linked up with the Blues on Monday ahead of a likely release from United this summer.
The centre-back featured in Pompey reserves' 2-1 win against Luton under-21s at Privett Park and caught the eye with an impressive display.
Taylor has already been through more than most aged just 21.
In November 2018, he was diagnosed with testicular cancer – only five months after signing his first professional contract.
However, Taylor made a full recovery, making his playing return for United's under-23s a year later.
At the time of his diagnosis, Mourinho was in the Old Trafford hot seat.
During Taylor's treatment, the Portuguese was sacked by the Red Devils before taking charge of Tottenham.
However, Mourinho vividly remembers when he found about about Taylor’s illness – and believes the Mancunian can inspire others.
He said: ‘It was a big shock for us at the time. He's a very sweet kid, a fantastic young professional and when we had news, everyone was in shock.
‘The first was to motivate everyone at United was him. He was the one who motivated all of us.
‘Lots of us were trying to hide tears when we knew it. He was the one who motivated us feeling strong and ready for this fight.
‘That was amazing, amazing news for the club (when Taylor was given the all clear) and all of us connected to him.
‘He won the biggest match of his career and everyone is happy.
‘It is an amazing story and an inspirational story for other young people that will find themself in a similar situation.’
Solskjaer succeeded Mourinho as United chief and was there to welcome back Taylor after his recovery.
He too couldn’t hide his delight and praised Taylor’s resolve and fortitude.
Solsjaer told the Manchester Evening News: ‘It's a fantastic story, to see him coming back.
‘I met Max very early after I got the job and to have seen his journey back to full fitness and the way he's conducted himself, and it's something he'll always have with him.
‘He's been through something no one should have to go through but he's come through the other end.
‘He's an inspiration for all the players. You can see when he's out on the pitch there's no fear anymore, he's had fear in his life, when you're on the football pitch you should enjoy yourself and I hope we can see him progress in his career.
‘It's a chance for us to give him extra motivation as well.’
Taylor admitted doubts he’d ever play football again during his treatment.
However, he came through his fight and believes it shows anything is possible
Speaking to Sky Sports, Taylor said: ‘I always had a mindset of that there's no way I'm not going to be alive after this," he said.
‘But there were times where I thought 'will I be able to play football after this?' And there were times where I thought there's no way I can get back to that.
‘But I think the message that I want to get out to everyone is it is possible - and it is possible to do more than what I've done after you've gone through such trauma.
‘It is possible to get back wherever you want to go.’
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