For the first time in his F1 career, Verstappen leads the championship following his recent victory in Monaco where Hamilton struggled to seventh after a poor weekend for Mercedes to fall four points adrift of his Red Bull rival.
Ahead of this weekend's Azerbaijan Grand Prix, however, Alonso has claimed there will be no change in the mindset of either driver due to the relative infancy of the championship after only five races and with another 18 remaining.
On the effect of Verstappen taking the lead, Alonso said: "Right now, in the sixth race, it means nothing.
"It will not change anything for Lewis or for Max. I am guessing if it is the last race it will change a little bit, it is better to be in front but in the sixth race, you are not thinking yet in the points."
Alonso warns Verstappen of Mercedes threat
Parallels can be drawn between Alonso's maiden world title and Verstappen's charge this season.
Alonso battled seven-time champion Michael Schumacher and his dominant Ferrari team whilst Verstappen is against Hamilton, who equalled Schumacher's seven-title haul last season, and the all-powerful Mercedes squad.
Asked if he felt ready to take on Schumacher in 2005, Alonso explained: "I think I felt ready before that but you never know what is going to happen in a championship.
"I felt ready, already, in 2003 probably to fight with the top guys and it is what we all feel here, I am sure.
"Any driver in the paddock thinks that with a competitive car he can be in a fight for the championship, at least I would like to imagine we all think so because if not, there is no reason to be here.
"I felt ready at that time but coming from the domination that Ferrari had for those years, you are always thinking they would bounce back and overtake in the championship on points but it was not the case so we took the championships."
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