Faith and Communities Minister Baroness Warsi said that politicians should "think long and hard" before embarking on any policy that might create confusion between illegal immigrants and members of ethnic minority communities who are entitled to be in the UK.
Mrs May last week announced that the van campaign would not be rolled out nationwide after a pilot in London showed it was "too much of a blunt instrument".
Lady Warsi said: "I don't think it was a particularly positive experience and I'm glad that we won't be going back to it.
"I think it's always important for Government to be clear that all people who are part of this nation legally are absolutely welcome.
" If there's anything we do in our policies which doesn't entirely make clear that distinction - anything that causes that confusion, we should think long and hard about."
It emerged last week that posters advising illegal immigrants to "go home" may still be displayed in immigration centres, including in Glasgow, despite the Government's decision to scrap the vans.
The Home Office has said the two schemes are entirely separate.