I feel sorry to say that even after putting a bounty none of the replies could reach my expectation. However, a reasonable amount of support goes for my answer 3) and I thank for that and I am grateful to the people providing additional thoughts. Hence I'll attempt to put my own understanding by collecting some of the arguments from the responses.
I think, in the beginning scientists more-or-less accepted the notion of wave having particle-like discrete behaviors. However, after the wave-particle duality hypothesis by de Broglie in 1924, people felt forced to look for wave-nature coming out of a particle. So de Broglie's hypothesis got its validity when electron diffraction was observed by Davisson, Germer, and Thomson. So diffraction and later interference by Jönsson became common tool to verify the existence wave nature of a quantum object.
Now one should remember that any object is quantum as quantum theory is valid in all time-space domains, but to see it's effect we may need to look at smaller systems. Since diffraction and interference are the ways to test the wave nature, on such experiments one needs slits of the size of the de Broglie wavelength. Let me pick up some of the issues below.
A) Wavelength of a large molecule (Fullerene) : The quantum interference on fullerene, whose radius is about 700 pico meter (7 Å) , has been done by Arnst group in Austria (https://vcq.quantum.at/fileadmin/Publications/2003-17.pdf). Now the temperature of the experiment was 900 K, which gives rise to most probable speed: $\bar{v}=\sqrt{2k_B T/m}=144\,\rm{m/s}$. However, the experiment uses a velocity filter and find most probable speed: $\bar{v}=200\,\rm{m/s}$. Using this one may expect: $\lambda_{\rm{dB}}=\frac{h}{m\bar{v}}=2.8\times 10^{-12}\,\rm{m}$.
From the paper we may find: $w=35\,\mu\rm{m}$, $D=1.25\,\rm{m}$, and $d=100\,\rm{nm}$ where they are fringe width, detector-to-gratings distance, and grating spacing respectively. Then using $\lambda=\frac{wd}{D}$ we find
$\lambda_{\rm{dB}}=\frac{35\times10^{-6}\,\rm{m}\times 10^{-7}\rm{m}}{1.25\,\rm{m}}=2.8\times10^{-12}\,\rm{m}$.
B) Infinite de Broglie wavelength paradox : As I asked whether $v=0$ permitted or not, one can recall that the wavelenth is the measurement of the periodicity in length dimension (say, distance between two repated peaks).
So when it becomes infinity, it means that the peak gets its next repetition at very large distance. That means no periodicity and hence wave nature is not detectable using our physical equipments. But getting bigger wavelenth by slowing down is the key idea of the ultracold atomic physics. Here average speed of atoms are discreased significantly by going up to a very low-temperature (see this: https://physics.aps.org/assets/e694a42b-2bf3-4a3c-98fe-66f55811896a/e10_1.png).
C) Uncertainty/wave packet argument against $v=0$ case: First of all, the argument doesn't hold for very large objects. Why it doesn't hold that could be a subject for debate on macro-realism (http://arxiv.org/abs/1412.6139). Secondly, one can always talk of expectation value even when quantum mechanics holds.
Thirdly, when we use wave packet argument to localize a quantum object, then we associate a group of waves, that implies that there is no single de Broglie wavelength, i.e. uncertainty remains in $\lambda$.
D) Earth's rotation effect: For an experimenter on earth this velocity contribution won't be detectable. Considering this only helps to avoid zero velocity situation.
E) My 3rd answer: Actually my 3rd answer not only works for human beings, it is the same any macroscopic stuff such as egg, baseball, bullet, etc for a given temperature. One crucial thing is that it is very difficult send such big objects through very narrow slits. Another important aspect one may consider: To see successful interference or diffraction pattern, the waves need to be
coherent. A discussion in Stackexchange has been made by John Rennie already.
So in one line (though it's not a conclusion), one can say, existence of de Broglie wavelength doesn't make much sense for human or other large objects since it cannot be tested within our present limitation.