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The Imps have reached the last 16 for the first time in 130 years.
Victory on Saturday would see them become the first non-league team to reach the quarter-finals since 1925.
"If we're realistic, we'd probably only beat them once in a hundred times but we've got to believe this is that one game," boss Danny Cowley said.
"We're going to be brave, we're going to fight and give it one hell of a go. If we do all of those things, we might give ourselves that chance.
"We've achieved the impossible to get here, we've just got to go and do it again."
Lincoln beat League One side Oldham and Championship teams Ipswich and Brighton to become the third non-league team to reach the fifth round since the turn of the century, after Crawley Town in 2010-11 and Luton Town in 2012-13.
Cowley, whose assistant at Lincoln is his brother Nicky, said that the competition had "fast-tracked our development."
"It's been brilliant and whenever this cup run ends, we will cherish what we have learned from it," he added. "It will hold us in really good stead for all of our futures."
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It's not too late to enter this year's FA People's Cup - as long as you do it by the deadline anyway - and that is at midnight on Sunday.
Entry is completely FREE, there are categories for everyone AND you can enter either as a team or an individual player.
Find out all the details here.

The Local Government Association is asking that councils in England be freed from restrictions on the ability to borrow to fund new home building.
It is also calling for powers to replace every council home that is sold off, as quickly as possible.
The government said it was delivering on its commitment to replace all properties sold on a one-for-one basis.
But in a submission to the Treasury, the LGA said the scale of the housing crisis demanded that action to fix the lack of affordable housing was taken immediately.
"The government's recent announcement of an additional Â£5bn investment in the form of loans to private sector organisations and for building homes on surplus public land is a welcome step," the LGA said.
"However, councils are also well placed to bridge the gap between housing need and future building levels and are keen to see - and support - delivery at speed."
The LGA wants to hold talks with ministers over whether councils' housing revenue accounts  - the accounts covering rents and assets - could be removed from the public sector debt book so as to enable borrowing against these assets.
"This would allow local government to rapidly contribute new homes in the market, meet a wide range of local needs and generate significant medium and long term returns," it said.
Councils also want powers to replace council homes that are sold off under Right to Buy arrangements.
Currently, the government only allows local authorities to keep 30% of the cost for replacement council homes.
This means councils cannot build replacements - especially as they are unable to borrow to fund the rest.
The call comes as new figures were released on the sales of social housing.
These revealed nearly 22,000 social housing dwellings were sold from 2015-16 - 12,557 by local authorities and a further 9,435 by housing associations.
The sales amount to about 0.5% of the total stock of four million social houses in England.
There was a particular spike in the percentage of housing association homes sold to private firms.
This was up 46% and government statisticians said this was likely to be because of housing associations taking a more active approach to managing their assets.
The Department for Communities and Local Government said it was delivering on its commitment to replace all properties sold on a one-for-one basis.
"As of June 2016, there had been 7,018 starts and acquisitions.
"This delivers more than a one for one replacement on the 4,369 additional sales since the scheme was reinvigorated in 2012."
National League leaders Lincoln City will aim to "achieve the impossible" against Premier League side Burnley in the FA Cup fifth round.
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Town hall bosses want urgent talks with the government on how they can rapidly build homes where they are needed.