No. Logistic regression models a categorical outcome, usually binary: it estimates the probability that y = 1, p = 1 / (1 + e^(−(w·x + b))). That output is continuous, between 0 and 1, but it is a class probability, not an estimate of a continuous quantity such as a price.
Example: linear regression can predict a house's sale price, say $412,000. Logistic regression answers a yes-or-no question, such as whether it sells above asking, with something like p = 0.73, which a 0.5 threshold turns into yes. It is fitted by minimizing log loss, built for 0/1 labels, so scikit-learn's LogisticRegression rejects a continuous target with an "Unknown label type" error.
The name comes from regressing the log-odds, which are linear in the features. Extensions stay categorical: multinomial logistic regression for several classes, ordinal for ordered ones. One exception: a proportion between 0 and 1, such as the share of employees joining a pension plan, can be modeled with fractional logistic regression. Otherwise, use linear regression or another regressor.