West Ham United boss
England international Jarvis is set to complete his move from Wolverhampton Wanderers, with the fee reported to be a club record £10.75 million ($16.35 million), including add-ons.
The 26-year-old is likely to be involved at the weekend against Swansea City provided the deal is completed in time and Allardyce did not hold back in his praise of the 26-year-old.
"Certainly from an attacking sense this is one of the best final-third crossers in the Premier League," he said. "His stats are extremely good and he delivers in the business end of the field.
"When you are trying to create in the Premier League and score goals, he is one of those players who can certainly give defences a really hard time and that is what we are hoping he can do for us."
Last season's facts do seem to back-up Allardyce's claims, as Jarvis attempted the most crosses in the top flight and had the highest cross completion rate.
Those statistics are even more remarkable given the fact he was playing in a side that finished bottom of the table and Allardyce is hoping Jarvis can contribute even more than an additional attacking threat.
He said: "It's a new dimension for us because this is a player of dribbling skills, pace, trickery, a player that not only provides chances but also relieves pressure on your defence.
"When he takes the ball he will keep hold of it and can take it from one end of the field to the other on his own and then produce a cross.
"And what that does is it stops the constant pressure that might come upon you in the Premier League. If you continue to give the ball away in the mid-term area the pressure comes back on the defence again.
"But if you give it to Matt he might not have anyone to find or pass to, but he will keep it himself.
"He will go up the pitch and take the opposition back into their own box and that's a critical part of being successful in this league, a player of his calibre and capabilities and it's something we don't have at this moment in time."
With the transfer window closing next week it is unlikely West Ham will bring in any more fresh faces, but Allardyce did suggest he would still like to add Liverpool and England striker Carroll to his front-line given half a chance.
The Hammers agreed a loan fee with Liverpool earlier in the month with a view to a permanent deal, but the 23-year-old did not want to move to
Allardyce, though, remains hopeful.
He said: "Many things in the final week of the transfer window emerge and should it be the case that we would be able to do something then I think it would probably only be a loan.
"We would see if we could pursue it and clinch it, but if we only finish with Matt and nobody else I would be happy with the squad I've got.
"While it is not quite as big as I'd like it to be, I think it has got a lot of quality.
"My problem is there may not be funds available for Andy now.
"If Andy became available or anybody became available and they wanted to join West Ham I would ask the owners. At the moment that is not the case and we just have to wait and see if and when that situation arises."
The former Newcastle United boss added: "If we play
"What isn't there is a proven Premier League goalscorer, apart from
English Premier League
Andy Carroll is on the brink of joining West Ham United permanently after passing a medical with the Premier League club.